Well if you're not concerned about a shared login, then of course you can easily install whatever forum software you wanted in a different directory and simply create links from your ClassiPress site. Compatibility wouldn't be an issue to consider because it would be separate anyway. It's really you personal choice if it "matters", but you have to consider from a customer perspective whether or not they would want to register/log in twice to use various parts of your website.
So ultimately, no it's not necessary, just perhaps better for the customer experience..
