The Beyond Atlantis 2 patch is different from the Atlantis 3 patch because the games installed into folders with different names. The Beyond Atlantis 2 patch is small enough that it was saved on the Web Archive of Dreamcatcher's site ***here***
The GOG version should be patched. Did you uninstall the Beyond Atlantis 2 version before installing the Atlantis 3 game from GOG?
According to ***Steve Ramsey's review of Atlantis 3 / Beyond Atlantis 2***
There was a patch available from Cryo, which the information says improves compatability with NVIDIA GeForce 2 and 3 video cards, and solves a freeze problem on faster (> 800Mhz) machines.
The patch is meant to fix the crash that happens when you speak to the guard early in the game. Is that where you're having trouble?
An old forum post suggested starting the game using Player 5 after installing the patch. Apparently it helped someone get past the crash-prone spot, though I don't know why.