I don't have any experience with IBB, but I've done a few cycles of HP Mass and I've got a decent amount of experience with rings (for someone who never did gymnastics seriously).
If you were going to include some ring work into your HP mass exercise selections (like ring push-ups for one of your Upper Body pressing exercises for example), then I think it would theoretically be possible. Realize though that you shouldn't be doing the ring exercises explosively (like CT advocates that you do for Upper Body pressing exercises on HP mass) so you might not get the same benefits as if you were to use more traditional lifts. Then again ring work does take a lot more total body coordination and tension so maybe it wouldn't be an issue.
I would not advise adding additional workouts involving ring work to HP mass, unless perhaps you had already done many cycles of it and felt that you had lots of extra energy to add in more workouts though out the week.
As far as ring work and injuries, if you do the correct progressions that shouldn't be an issue. People generally get hurt because they try to rush ahead to exercises that they aren't ready for. I'd second the recommendation of getting Coach Sommers's book as it will point you in the right direction as far as progressions go.