Would it though? Would a guy like Lebron be a better fighter than say, Walt Harris? If so, why? I'm not saying having NFL and NBA athletes pick up MMA young wouldn't raise the bar some, especially given the absolutely terrible state of HW MMA now, but I don't see it as being as cut and dried as you make it sound. For starters, MMA really is not for everyone, or even most normal people. Those athletes that pursue it might find they simply do not like the grind and toll it takes on... everything, really. The ones that make it through years of training would have a leg up in certain areas compared to the fat Polskas they fish out of Eastern Europe for random Fight Night cards, but I don't know that the game would look all that different in the end.
Just my take.