Let me preface with this ...by no means am I an expert at anything related to fighting or training... so bear with me as I give my un-educated, completely speculative opinion.
if your intent is to swing a bat as fast and as hard as possible... then your brain has to trigger the correct muscles to maintain the bat at a particular level and contract at the appropriate time with maximum force.
When you put a weight on the bat, you brain is triggering different muscles to compensate for the increased 'downward' force to keep the bat level... this has little to no impact, IMHO, for increasing performance of swinging a non weighted bat... but could actually be detrimental since it changes the parameters the brain was initially considering with the weight off.
That said, I think weights and training have a symbiotic relationship... depending on your end goal.
IMHO, technique is the foundation to build on. Weight training supplements technique. Rarely do you find successful mma fighters that start off as power lifters (although some try their hand it it).
But obviously power comes into play when dealing with opponents that are as technically savy as yourself.
IMHO, weight training can help fine tune an mma fighter... give an edge when necessary... the caveat is to not be overly dependent on that factor. ie. expecting to simply be the stronger of the two.