If he had a clean record prior to that conviction and has stayed out of trouble ever since, I don't see why his naturalization application will be turned down. Sure, there will be some questioning and probably some extra background check, but his application could be granted.
The irony is that we have a President and a Vice-President who are "convicted criminals" -if you go by the law- and they are holding the highest positions in the country. This had never happened before in the history of the United States.
Bush was arrested and convicted of DIU. Prior to that he had been found guilty of "disorderly conduct", which is not such a big deal, but it is a conviction nonetheless. And before that, Michael Moore claims that Mr. President got caught stealing from a hotel when he was in his late teens...
Loveanh, contact a lawyer with your doubts and have some legal opinion on whether this can truly jeopardize your citizenship. I have a neighbor who got citizenship last year and he had been convicted a couple of times of some minor crimes. The most serious one was a felony (he was carrying some sort of weapon) and the last conviction came in 1999 when he punched a cop in the face after the officer allegedly disrespected him. Amazingly, his application was approved. He himself could not believe it! Unless you were found guilty of an aggravated felony, there may be a chance that your citizenship is granted. Give it a try!
Einmalig