Nope. You can subscribe/post/comment on any community on any instance. There is one small seam though: if you're the first person to subscribe from your instance, you need to put in the full URL of the community (https://lemmy.ml/c/gaming, for example) to pull it into your instance.
After that, everybody on the same instance as you will see it when searching for communities just like it was local.
EDIT: Oh, forgot to mention: make sure the search is set to "All", not "Communities" when you do this.