If Obama provided a falsified birth certificate, is that sufficient grounds for impeachment?
There are two issues you raise together. One is the crimes of forgery and fraud for which he could be impeached. The other related issue is whether he is constitutionally eligible, once his actual birth location and parents are identified.
There is a theory that if Obama was never qualified to be president, then he actually could not be impeached because that is reserved for actual presidents, not usurper occupants in the WH.
We do not know whether the actual birth location and identity of Barry's parents will prove to be qualifying or disqualifying according to SCOTUS when they hear it if they hear it so we don't know whether he is qualified to be impeached or removed.
If Barry is personally implicated in directing the forgery and fraud I would think that even the Democrats would go down to the WH and tell Barry that the game was up.