A very well documented example of a small celestial object with a gas giant is the collision between Comet Shoemaker-Levy 9 with Jupiter. As it was a comet that was tracked, the whole process of the collision was well documented and observed.
Though the collision occurred in July, 1994 - the first effects occurred 2 years earlier, according to the NASA Technical Report "Shoemaker-Levy 9 and the tidal disruption of comets", when the
break-up of Periodic Comet Shoemaker-Levy 9 into multiple pieces following its grazing encounter with Jupiter
This represents one of the first stages of the collision that could occur as the celestial object approached the large planet. In this case, this breakup resulted in Comet Shoemaker-Levy 9 to form a train of fragments to eventually collide into Jupiter - the full process at this stage is shown in the diagram below:
Image Source: Tufts University
The train of fragments was captured by the Hubble Space Telescope (shown below):
Image Source: NASA
Each fragment was designated a letter (e.g. Fragment A etc). According to the article "The collision of Jupiter and Comet Shoemaker-Levy 9." (Zahnle and Mac Low, 1994), these fragments were in the order of about 100 m to 5 km in size, heading straight towards Jupiter.
Then to the main event - the collision of the comet fragments with Jupiter.
An example was from Fragment G, one of the larger fragments, when it collided with Jupiter (image below):
Image source: NASA
As you can see, the explosion was spectacular - about 21 fragments impacted into Jupiter over a number of days, given Jupiter's relatively fast rotation, the impacts became quite distributed on the top of the clouds of Jupiter, as shown in the ultraviolet image below (the circle shadow below is the moon Io):
Image Source Air and Space Museum
There have been several impacts into Jupiter (and presumably into the other gas/ice giants as well), another one that underwent scientific scrutiny was an asteroid 'the size of the Titanic' colliding with Jupiter in 2009, reported in the article "New evidence that asteroid, not comet, struck Jupiter in 2009", describes a comparison between the 2009 asteroid and Comet Shoemaker-Levy 9 are described as:
The dark debris, the heated atmosphere and upwelling of ammonia were similar for this impact and Shoemaker-Levy, but the debris plume in this case didn't reach such high altitudes, didn't heat the high stratosphere, and contained signatures for hydrocarbons, silicates and silicas that weren't seen before. The presence of hydrocarbons, and the absence of carbon monoxide, provide strong evidence for a water-depleted impactor in 2009.
Overall, the article mentioned the likely process during any collisions of a celestial body with a gaseous planet, using the example from Jupiter:
Plunging through Jupiter's atmosphere, the object created a channel of super-heated atmospheric gases and debris. An explosion deep below the clouds – probably releasing at least around 200 trillion trillion ergs of energy, or more than 5 gigatons of TNT
and the celestial object itself - vaporised, totally destroyed in the resulting explosion.