What could have happened? That the other families would have sided with Solozzo to avoid a long, costly war? Or that Sonny would make the deal if hs father died?

Both were credible scenarios. It appears, from the film and the book, that the other families did take sides against the Corleones. The book says that, after the murder of Sol and Mac, the police clamped down on all Mob operations. The families sent an emissary to Sonny and Tom asking if they would give up the murderer. When they refused, "...the Five Families War of 1946" commenced.

Sonny's temper, and perhaps his guilt in knowing that his gaffe at the drugs meeting emboldened Sol to strike at Vito, may have hardened him against making any deal with Sol under any circumstances. But if Vito died, he'd be under tremendous pressure from Tom and the caporegimes to stop the war and get back to business. The Corleones couldn't run on empty indefinitely, and they'd need income from drugs and other sources to rebuild the police/political capital they'd lost due to Vito's death. I think it's at least possible that Sonny would have made a deal.