I don't know about Gen 2, but I tested it for Gens 3 and 4, and it would appear that transform does copy the capture rate.
For Gen 3, I tested using rattata as the transform subject before switching to a False Swiper, and captured the Dittos using Great Balls (they were the only balls I had on me and I'm too poor to buy regular Pokeballs in LeafGreen :P). When at 1% health, it is impossible for rattata to escape a Great Ball. However, Ditto only has a 23.4% chance of being caught under these conditions. I managed to catch 5 in a row, so transform almost definitely copies catch rate in Gen 3.
My tests for Gen 4 were nearly identical to LeafGreen, except that I used a Shinx (which has the same catch rate as Rattata) and pokeballs. Once again, at 1% HP, Shinx has a 100% capture rate, but Ditto now only has a 14.3% chance, due to the weaker ball. Nonetheless, I was still able to catch 5 in a row, so we can conclude that transform in Gen 4 (almost definitely) copies catch rate.
Edit: turns out, Shinx's catch rate is a little bit lower than Rattata (235 instead of 255), but at 1% HP, a pokeball is still guaranteed to work. So yeah, doesn't change the conclusion of the answer.