If the situation were reversed, if Israel was fighting with hand weapons and Arafat had atomic bombs, what do you think the result would be?
With IFs you can put Paris in a bottle.

If the Palestinians had the atomic bomb in 1947, Israel would not exist as it would not have become a country.
If the Palestinians had the A bomb after 1947 but before 1967, the Israeli borders would still be the same as those before 1967. And Israel would still exist as it was recognized as a nation by the UN.

The A bomb is a way to prevent invasion and attacks, not necessarily a way to attack the other side.
If Palestinians had the A bomb since intifada started, there would be no need for suicide bombers, and they'd be respected. No need for terrorist groups either.
Suicide bombers are a sign of desperation, not a sign of confidence which owning the A bomb would be.
It's all psychology.