I hand-paddle often, unless I need the power to push through big holes or waves. You'll flip more, because your brace is weaker, and you don't have as much power. I use paddle-gloves, but I can flip bare-handed, or even with just one hand without problem (pear shaped girls unite!). Sometimes even if I have my paddle, I'll drop it to roll quicker with my hands, which is kind of a bad habit, because then I have to grab my paddle again, assuming it hasn't floated away.
The point is, you can flip pretty easily paddle-free if you really work on a good hip flick. I flip mostly with just my hips. Guys have it harder, but if you practice that, you barely need to use your arms anyways (unless you're in something really rough, stuck, etc), so you can save your shoulder!
If you're wondering how to do it, find almost any girl at the pool session and ask her.
*edit*- and as far as boofing or anything else goes, you can definitely play, surf, and squirt - it's just harder, and will require much more use of your shoulder than a roll likely would. I don't know about boofing, I could never do that even with a paddle.