For all practical purposes,Neil was a Boss equal to Big Paul. When Gambino passed him over,Neil was given control over the traditional blue collar Mob rackets by Castellano,to keep the peace and to keep Neil happy.Paulie knew better than to cross him.

I believe that Neil anticipated Paulie going away for a long time.Perhaps he felt that if he could bide his time until then,he could make a good case for taking over the Family.

If the Boss spot became vacant,I think that Neil would have moved into it,if not by popular vote,then by sheer force.
To do this,he would need an ally like Gotti,who was feared,ruthless,and above all,loyal to Neil.Keeping Gotti happy would be good strategy.

Had he lived, I think Neil would have been the next Gambino Boss,and Gotti would have been named Underboss. Neil saw Gotti's crew not as troublemakers,but as old school,ruthless thugs,much in Neil's own image.Had Paul vacated the top spot,these are the guys Neil would want in his personal army.