Not to my knowledge. I think that CIG paid an all out license fee to be able to take CryEngine and run with it in any direction they please without any feedback from Crytek. They hired former Crytek engineers that had been with the company since the original Far Cry and Crysis days. I guess Crytek was downsizing and it was a perfect time to scoop them up.
I can't imagine how much "consulting" Crytek could do given how modified it is now and how much experience they let go. As for bugs, I doubt anything CIG come across would be applicable to other implementations. CR has said himself that CryEngine was the best of the options they had available at the time, but through development they're going to be nearly rewriting the entire engine by the time its done. It's a single player FPS engine being asked to do a MMO space sim. The network efficiency overhaul alone is affecting every aspect of the engine except the render pipeline itself, and they've already put work in there.