At least one of the gods depends on a player's two workers being distinguishable from one another (Selene can build with her female worker even when she didn't move), so that might not work with the old edition. And many of the Golden Fleece gods need other further components that you'd have to improvise. But most of the base game gods should be playable no matter what your set looks like.
Edited to add: I haven't played the variant with a Golden Fleece, so I don't know if you're missing anything, but that should be easy to improvise too, if you want to try it. (You could even use a building block on its edge or something similar.)
Ah thanks for the tip about the need to distinguish between workers for a few gods. Will keep that in mind.