I think Brady could do well here, he's a master of the short passing game and I think Brown and Davis could take advantage of that with their YAC ability. Plus he would bring so much experience and be able to teach this team a lot about winning.
Why I would be hesitant, is that you're going to get one, maybe two years from Brady? and then transition to another QB. Where, if Tannehill is the real deal, he could provide some consistency at the position for the next 5-6 seasons. Having a QB with that much knowledge and experience in a system is incredibly huge and could let the offense really grow into something special, beyond just pounding it with Henry and play action.