Did Obama deliberately time his birth certificate release with killing Osama?

[ZuWo]

That's an interesting hypothesis. Yes, it seems possible that he released his birth certificate just shortly before Osama bin Laden was killed in order to highlight that he's a real American and a tough leader.
On the other hand, there was no guarantee that the secret mission to execute Osama would turn out successfully. If the mission had failed, releasing his birth certificate wouldn't have had any positive impact at all.