I just finished Gen Chem and am now doing Ochem I and II over the summer and there's really nothing I learned in Gen Chem II that would've helped me tremendously in Ochem I.
There are some concepts that overlap, but if you don't take Gen Chem II you're not going to be screwed. If your chemistry is super rusty, then you may have to take an extra hour to learn the background, but it's not in-depth and not something you can't learn on your own very, very quickly (hour tops). You don't need to know anything super well as long as you understand trends and stuff like that (no ICE tables, calculations, but trends instead).
Depending on the book used by your professor, you'll cover different things in Gen Chem II than I did, so take a look at the syllabus.
Overall, though, for Ochem I, the useful things from Gen Chem II were the following:
- Equilibrium constants: the general idea of what they are.
- Acids and bases: very very basic stuff such as knowing what a pKa is, strong acids v. weak acids, definitions of Bronsted and Lewis acids/bases and nucleophile v. electrophile (although this is discussed in Ochem I briefly so it should be taught to you), and the fact that the equilibrium favors strong acids over weak ones
- Nomenclature: very little covered in Gen Chem, and we started from scratch in Ochem I so you'll be ok
I think that's about it. Overall, you should be fine, IMO.
At least in our Gen Chem II, we didn't cover mechanisms in the way Ochem I uses them (or maybe I just don't remember doing them), so we really had to learn them all over again, which was fine since it was part of the ochem syllabus anyways.