correct sentence

Grammatically, yes. I don't think you need the comma.

The purist might say (and that's not me, maybe he/she will turn up soon) that the correct form of that sentence is

Only by coming together will we overcome these obstacles.

I think that's a little more elegant: but I agree that the first example does not seem wrong.

Only by coming (how about: working, banding) together will we overcome these obstacles.