Who was even at the convention, is one question. This wasn't quite the era where the candidates didn't show up, but neither was it quite the era where being there was a mandatory part of getting the nod.
In the end, I don't think it would change Roosevelt's victory. But if the perpetrators are actually found, their identities could have big effects, if they're communists, fascists, German agents, I don't know. You can come up with some interesting possibilities there.
What about the fact it was a bombing, what were party relations like back then?
Would the Republicans try to pin it on the Democratic party?
I think that's way, way beyond the pale for 1940.
They give the nomination to Charles Lindbergh. FDR still wins. Lindbergh is a piece of work gives up his officers commission in Army Air Corp. But keeps his NAZI decoration.
I think the fact that he had only just returned to America after previously leaving in a huff, insulting the entire country in the process, would be a bigger obstacle than his Nazi medal.