I will say when I used to train MMA back in the day,.. my BB routine was virtually stayed the same. For the longest time it work great, but the intense training schedule of BOTH causing extreme over training. Combine both with a nearly full time job, and full time college,....its very hard to do both, and get good gains in both, but its do-able, depending on your schedule. Just mess around with your routine and diet to best accommodate the MMA training, and maybe think about limiting w/o's to power exercises, and fighting specific exercises only, like DB punches, medicine ball throws/ sledgehammers, weighted knees/kicks, etc, etc.
I can say on many of the guys I grappled who wrestled or grappled for years, I held my own with almost all of them, due to my hip/leg strength and flexibility, although my main experience was in kickboxing/muay thai, which works well with my size and height. I think its more of a combination of technique, then having the strength and speed execute and finish off what you are doing.