I own the original Doom3 and I wouldn't pay to buy the same game simply for the sake of having the Steam version.

So my question is, does the steam version of Resurrection of Evil work with non-steam Doom3? Can I just copy the pk3 files and paste them to my Doom3 and get it running?

I don't think it's compatible BUT right now the Doom 3 pack, which contains both Doom 3 and Ressurection of Evil is available on Steam for $3.24 USD!!