Well I'm certainly not fit, but yeah my coach can grapple for ages while my arms get pumped and I get wasted. It's all technique though, without the technique you're just powering everything out.
I don't get injuries; we spend about 10-15 minutes rolling up and moving about before doing anything. You rarely start doing anything intensely (unlike squatting first thing in your workout) so it ramps up quite nicely. We don't use gi, it's all practical stuff for MMA.
Also, there's no AC in my gym, which I find is fucking awesome because it makes my muscles and joints much better. I don't have to do half as many warm-up sets in weight training because I'm already hot and dripping sweat.