Vince would have eventually allowed Savage to wrestle, but it would have been much later on. After Hall and Nash left, WWF needed top guys. You have on sitting there in the Macho Man.
Macho vs Mankind, Undertaker, Triple H, Kane, Austin and even The Rock all could have been possible. Savage's skill as a wrestler had depleted in the late 90s. We're also talking about a timeline where Savage may have primarily been an announcer from 1994 to 1996/97. That's about two to three extra years of inactivity.
Savage would have likely been involved in the Corporation angle. I doubt he would have joined DX at any given time. Macho Man would have been a heel mouthpiece in the group, eventually feuding with Stone Cold.
It's unlikely Macho Man ever would have recaptured the WWF title had he stayed, but IC, tag, and European titles would have been possible. I doubt he would have held the hardcore title.
Macho Man might have stayed with WWF through to his death in 2011. He would have likely replaced Jerry Lawler for much of the late 90s as colour commentary. Imagine Macho working with JR calling the Mankind Hell in a Cell dive.
Macho likely would have permanently retired not long after the Invasion. Jerry Lawler would have been a secondary commentator to him. During the first brand extension in 2002, Macho would have stayed on Raw while Lawler would have gone to Smackdown with Cole. Taz never would have become a commentator.
Macho would have called nWo matches, while never having interacted with them in WCW. Macho would have been on the mic when Punk won his first title, same for Batista and others.
One would have to wonder if Macho Man would have died in 2011. What if he had his heart attack on air like Jerry Lawler did? Or somewhere on the road with WWE medical staff nearby.
It's interesting to think what could have been. I think Macho would have made a great corporate heel before turning face during the Invasion. He would have been around for a lot of those classic moments like Hell in a Cell, Austin, and DX. The truth is though Randy Savage wanted to be the Macho Man, and the Macho Man doesn't just sit there calling the action. He is the action, oh-yeah.