I like the guy, but I'm not sure how effective he would be. After WWII, American political life made a hard right-wing turn, with fear of the Soviets not making things easier. Everyone is paranoid the Reds are about to invade, and the President is (perceived as) chummy with them? No way he's winning the 1948 election. Hell, he might not even last that long. The GOP Congress that gets elected in 1946 may just impeach him. And I don't think he had a great many allies within the Democratic Party who'd be willing to defend him. His unpopularity within the party was why he was dropped from the ticket in '44.
The only thing I can say for certain is that he wouldn't have dropped the A-Bombs on Japan. How that would turn out, I'm not sure. Between the Soviet declaration of war and the fact that Japanese society was already on the brink of collapse due to aerial bombardments and being on the edge of mass starvation, I think Japan would've surrendered eventually. It's just a question of how long and how many deaths. Too many what-ifs to figure out in there.