Could Olympus Mons have thrown ejecta out of Mars' orbit when it was active? Does it fit with the composition and dating of meteorites with martian origin?
Since this has gone unanswered, I'm going to give it a shot.
Probably the answer is no. We know that on some moons, volcanic eruptions do send material into space.
Enceladus for example, feeds Saturn's E-ring. It regularly shoots about 200 KG per second into space.
The other highly volcanic moon in our solar system is Io which shoots material high into it's orbit, and it has some of the largest if not the largest observed volcanic eruptions. Source: http://www.space.com/26732-jupiter-moon-io-volcano-eruption-photos.html
But I couldn't find any references that Io's volcanoes shot material into orbit. short article on Jupiter's rings
The difference between Enceladus and Io is size. Enceladus's escape velocity is 0.239 km/s (860.4 km/h) Source in link above, and it's gravitation is just over 1% of Earth's. Io's escape velocity is 2.558 km/s and it's gravity is similar to the Moon's, about 18% of earth's. If Io has a hard time sending volcanic material into orbit, on Mars, it would be nearly impossible.
Io can shoot material up to 300 miles into the air, Source: https://en.wikipedia.org/wiki/Volcanology_of_Io but that's still only about 1/7th to 1/8th of it's radius, probably well within it's Sphere of Influence. On Mars, it's Sphere of influence is significantly larger and it's gravity twice as much. If a super large Volcano shot material 300 miles into the air above Mars, that's still well below escape velocity. (I could run the Maths if you like, but in a nutshell, escape velocity changes with the square of the distance, so, ignoring air resistance, Io's enormous eruption reaches 14% of it's diameter or 28% of the radius is about 40% of escape velocity - assuming I got my math right. On the Mars, an equivalent enormous eruption would be what, 20% of necessary escape velocity? Less?
Also, while Olympus Mons is enormous, it didn't all erupt at once. Source: http://www.space.com/20133-olympus-mons-giant-mountain-of-mars.html
Olympus Mons is over a hot spot on Mars, subject to regular volcanic eruptions (regular meaning, perhaps every few million years), but because Mars doesn't have plate movement, the eruptions happen in the roughly the same location and that, in combination with virtually no erosion and low gravity, is why Mons is as large as it is. It probably does erupt impressively when it goes, but I'd be pretty skeptical that it erupts violently enough to send magma into space.
Also, most of the Martian meteors on Earth are from a recent impact, about 5 million years ago: http://www.space.com/24962-mars-meteorites-single-impact.html Olympus Mons may have erupted about 5 million years ago, so the timing works, but I still think it's unlikely.
(I could add some links on how far Earth volcanoes can send magma/pumice if interested, I looked that up as well).
To get that kind of velocity, you need significant amounts of concentrated energy. A gun works by creating a controlled explosion with only one place for the energy to go. Rockets work by sustained acceleration over time. While it seems quite different, a meteor strike is similar in some ways to an enormous gun. When a meteor strikes the surface of a planet, it hits with so much force in a localized area that the ground get's crushed and then rebounds with enormous force in a localized area. A volcano simply can't (I think) generate that kind of concentrated energy unless it's very low gravity like Enceladus, 1.1% of the gravity of Earth.
That probably needs tidying up a little. I'll try to clean it up later.
A somewhat related conversations on this subject if interested: http://www.reddit.com/r/askscience/comments/1gkiz3/could_a_volcano_eruption_theoretically_be/
The short answer to your question is, "no," and that's for a couple reasons.
There are a lot of different styles of volcanism, but they can be broadly classified as "pyroclastic" and "effusive." Pyroclastic is your classic volcanic eruption that looks like an explosion out the top. Effusive is more like a pot on the stove that keeps boiling over. While some early volcanism on Mars was pyroclastic, volcanism over the last ~4 billion years has been mostly effusive. That means that Olympus Mons' eruptions would not have been flinging material high enough and with enough velocity to make it unbound to Mars' gravity.
That and the fact that at least Earth-based pyroclastic eruptions tend to eject material on the order of 100 meters per second, and Mars' escape velocity is about 5 kilometers per second, so you can't get enough speed.
It is entirely possible that some of the meteorites came from ejecta launched by a crater formation on a volcanic surface, such as Olympus Mons, however. The nakhlites (a type of Martian Meteorite) are volcanic, and they date to around 1.4 Gyr. Olympus Mons has some material that dates to roughly this time, though the main calderas are much younger (the oldest having a surface age of ~400 Myr). But, a meteor hitting Mars will dig down and can excavate older flows.
So, the longer conclusion-answer to your question is: No, the eruptions of volcanoes on Mars - including Olympus Mons - cannot be responsible for the Martian meteorites seen on Earth, but it is certain that volcanic material from Mars has formed some of the Martian meteorites, and it is possible that some of that volcanic material we have on Earth today is from Olympus Mons.