IMHO, I don't think Neil had any desire to be Boss. He didn't need the heat,and he pretty much already was a Boss. He ran his own Family-within-a-Family,answered to nobody,and made a ton of money.
I think he would have thrown his support behind one of the more respected Captains and stayed on as Underboss, just like he did with Carlo and Paul. Bilotti would have been knocked down by the new (acting) Boss,and Paul would be given the courtesy title of Boss until he died in jail. Nobody liked or respected Bilotti,whereas Neil was well respected by many Family members,and feared by the rest.
Ideally,Failla becomes new Boss,takes over Paul's "white collar" rackets,Neil is Undeboss,running the same rackets he's always had.and Gotti becomes a powerful Capo and ferocious earner. Oh,and Billoti winds up in a meat grinder,because he won't stop squawking about the new administration.