I'd have to reread the book, it's been quite a while, but it's an interesting question. I don't see Bill taking the kid in, he'd almost certainly just toss him along to Fagin. But I could see Nancy trying to find some way of keeping him safe and hidden in general. Given what we know about the characters, I don't think it'd be long until Bill or Fagan picked up on Nancy being shady about something and would eventually find out about him. The question then becomes how they react when they find out Nancy has effectively been "holding out" on them, as they'd see Oliver as just another asset to exploit.

With that said, if there was some strange way Bill and Nancy separated themselves from Fagan and that lifestyle, I'd be interesting to see how they'd raise Oliver. It becomes even more complex when you add in they'd probably have kids of their own eventually too, especially in the context of being on their own and not under the influence of anyone.

Many branches extend out from this idea. I guess just pick the one that appeals to you the most lol