The same as Republicans did for Clinton and look how lovely that turned out.
From what I understand of the system, even if they impeach they would need a very strong majority to get it through, its a political decision, right? The democrats will most likely do it anyway, but only if the reps drop Trump, they will get it through.
I'd say..
Pros for them: Pence will be new big dog, which they would have preferred all along.
Negatives for them: Voters will punish em for that and they can kiss at least the next vote good bye.
They'd need a strong conviction to really do that. The system is weird anyway, if a pres is removed you should have new elections, not a ladder of succession.