What are the chances neutering will help with this issue?

No this is a learned behaviour, he is shown a stimuli and now has a programmed "response". the dog is most likely snapping because he found it got results. instead he needs to be enrolled into a good behaviour class, and one with some safe dogs so he can relearn this behavior. for now, muzzle him, or keep him on-leash at all times.

Male dogs to male dogs, regardless of being intact or not, are far more prone to fighting. same with female to female. avoid male dogs.

It could help but it might also not help solve the problem completely. One thing you might do to see if he's completely comfortable around the dog at all is having them meet in neutral territory - a park, someone else's house, etc. Somewhere where neither of the dogs lives, though. Training can help as well and doing positive association. Get a favorite treat and have him focus on that when he's around the other dog or dogs by having him do tricks (simple ones - sitting, laying down, etc). Feed him his favorite foods when he's around the other dog so he'll smell the other dog and be eating, associating being around the other dog is a good thing.

These should be able to help him realize that it's okay to be around the other dog. There is a difference between being an alpha and just plain being scared - it sounds like he's just scared since you said he was bullied and not properly socialized with other dogs, which is the same thing that happened with my dog. He's probably snapping because he wants the other dog to stay away. Most of the time when a dog is taking over another dog as alpha they don't snap unless the other dog challenges him/her. He might also snap at the other dog if they're trying to play with him and he's scared.

Basically, if he's doing more than growling (since dogs usually don't actually fight over dominance), and snaps quickly, he's most likely scared.

First of all, your animal is not trying to be an "alpha". Unlike what you read here, dogs are NOT pack animals, nor do they work as a pack when there are more than one of them. Owners need to take a leader role in order for a dog to understand what is expected and wanted of them, not just to "dominate" them.

Please read this article;

http://www.4pawsu.com/alphawolf.pdf

David Mech is the one that started all this erroneous information about behavior and pack. He has since changed his mind and this article explains it.