I like this plan, and it can work, but you have to hit it the right way.
Gymnast, for the most part don't bench. but they do work there upper bodies a lot with dipping type moves, pressing type moves, and flye type moves.
Preses to the front
Side, and rear laterals
Medium grip chins
Make delt training the number one priority, and do all your chest training after you have trained delts. Think in terms of how a gymnast trains.
Go heavy on your abs as well.
Check out Yuri Van Gelder. Dutch gymanst who specializes in rings.