It takes an infinite amount of time for something to fall past the event horizon of a black hole from the perspective of someone outside the event horizon. Black holes also evaporate after a finite amount of time from an outsider's perspective due to Hawking radiation.
Does this mean that you would never actually reach the event horizon if you fell into a black hole because the black hole would evaporate?
I've asked this question to a couple of physicists a few days ago. Great minds think alike, huh?
First, bear in mind that Hawking radiation is only hypothetical. It is not theory. If we trust that hypothesis, this is what we can get.
In general relativity, black holes can be described through a number of approximations. For example, the Schwarzschild solution for a black hole describes it as an eternal object — not something that exists for some times, and doesn't exist for others. According to this solution, the event horizon must have always existed, and must remain existing eternally.
Schwarzschild black holes approximate black holes very accurately, but as you can tell, they fail to explain how a black hole can form, and (assuming Hawking radiation is real) they don't explain how one could eventually evaporate.
Of course, that solution won't help us. I've kept looking for one that accurately describes an evaporating, creatable black hole, but I've found nothing. The conclusion I've come to, along with those I've asked, is that our question has a major problem: Hawking radiation is explained via quantum field theory.
Thus, you can't simply use a GR solution for a black hole; you'd need some unholy mixture of quantum field theory and general relativity (keep in mind that both GR and QFT are incompatible in many situations).
In the end, it all comes down to how little we really know about black holes. It's not really possible to determine which solution is the best, and our inability to reconcile QFT with GR poses a big problem. The best answer I could give is "nobody really knows what would happen if you kept approaching a black hole".
We don't know if we would reach the event horizon, we don't know if the black hole will evaporate. We simply don't understand them well enough to know what solution would work, or how we would put QFT into it. If we somehow managed to find an approximation that properly combines GR and QFT, I assume (but don't quote me on this) the situation you described would be possible.
If it is possible, by the way, then we could confidently say that a black hole of any size could rip you apart through tidal forces. Tidal forces become weaker as the black hole's size increases, so one would assume a large enough black hole wouldn't rip you apart.
However, if we take Hawking radiation into account, and if your proposed scenario were indeed correct, the black hole would shrink as it evaporates. Since it would get smaller at a faster rate as we approach the event horizon, it would soon be small enough to rip us apart.
As it has been mentioned in a comment by @zephyr, the infinite time issue is actually a non-issue.
As you move closer to a black hole, the relative time to your point of view doesn't change in the same way that it does from a different reference frame.
Looking at your own situation, everything would happen in "real time" however, everything observed about you and your situation would take "and infinite amount of seconds for one second to pass."
This is also a contested issue because there have been measurements and possibly observations (I'd have to fact check this) of stars "falling" into black holes. So the infinite time from the outside observers perspective is also not possible.
In short, the best way to answer your question without going to much into theory, hypotheticals, or mad science, is simply to state: No, it does not mean that.
The event horizon never forms (nor does the singularity) because of general relativity which dictates gravitational time dilation. There is no universe within the black hole as some speculate. As the gravity becomes more and more intense time slows relative to the rest of the universe. A really large black hole radiates Hawking radiation at a temperature that is quite cool, for a supermassive black hole with millions of solar masses that temperature it's radiating at is $1.4*10^{-14}$ Kelvin or lower (it's about $10^{-7}$ or $10^{-8}$ for most stellar black holes). But here's the caveat, the Cosmic Microwave Background is at about 2.7 Kelvin so even accounting for the fact that black holes will only absorb CMB radiation that's a direct hit (otherwise it will orbit and miss being captured), it still means that all stellar mass or larger black holes are currently gaining more mass/energy from the CMB than they are losing to Hawking Radiation.
Since the universe continues to expand and is accelerating, the CMB will fall below $1 * 10^{-8}$ Kelvin in about $10^{29}$ years, at that point stellar mass black holes will start losing mass/energy and shrinking. Around $10^{36}$ years it'll fall below $10^{-14}$ and supermassive blackholes will start to shrink. The smallest stellar mass blackholes will finish evaporation around $10^{68}$ years from now and the largest around $10^{103}$ years. Another fun fact is that the Hawking radiation picks up in speed as the black hole evaporates and all black holes "explode" with the same amount of force calculated as the amount of radiation they release over the last second of their life, it equal to about 250,000 Tsar Bomba H-bombs or about 5 trillion tons of TNT. The only black holes that wouldn't explode with this much force would be microscopic ones which evaporate in less than a second.
So we've established that black holes will all eventually evaporate...it takes a ridiculous amount of time but it does happen in a finite amount of time. And as the matter falls in to form the singularity and event horizon general relativity shows that time dilation becomes greater and greater with respect to the rest of the universe. It becomes so dilated that if you were falling into a super massive black hole you would the hold get larger and larger, until a point when it took up half of your view then the rest of the cosmos would appear in a circle behind you, growing smaller and smaller as you got closer and close to the (not yet formed) event horizon. If you were to use a telescope and zoom in on that ever shrinking circle you would notice a few things. All the light falling into the black hole would get shifted bluer and bluer, time is going by much faster out there than where you are located. Before it blueshifted beyond visible light you might just be able to see starts actually moving in your host galaxy, if you had a computer with you and special detectors to see gamma rays (because light would continue to shift into harder and harder gamma rays) you would be able to watch trillions of years go by and it would keep speeding up faster and faster and faster, you could watch every star and galaxy in the universe go nova or super nova (that would be spectacular to see the stars popping like fireworks rapidly) and eventually that would stop and the sky would just be black, not because you've crossed the event horizon but because there are no more stars left. On the outside the majority of your fall towards the black hole would be in darkness with no stars or galaxies left, but from your point of view it would only a small part as your clock has slowed down so much that it would pass in moments. You will eventually arrive at where the event horizon should have been but the event horizon will have started shrinking at this point as the black hole has finally started radiating away more mass/energy than it's taking in from the CMB. You'll continue to move towards this new shrinking event horizon (this will all take mere moments form your point of view) until you get blasted with and explosion as described above. Actually the explosion will seem much greater to you, as the entire mass/energy of the black hole will seem to be released pretty much all at once due to your dilated frame of reference, for a super massive black hole. Calculated the force in megatons for a typical 50 million solar mass black hole, that's about $4 * 10^{40}$ megatons of TNT or $4*10^{38}$ Tsar Bomba's going off all at once from your reference frame.
You never cross the event horizon, it didn't have enough time to form as it would take infinite time and black holes eventually evaporate.
