This is a very risky proposition because of the risk that poloinex will recover your account back to you. I would think that it would not take much more than a signed message from a withdrawal and/or deposit address for you to have full control over the account.
How? In minutes? they will recovery in minutes? And why? I'm just want to reduce my losses..
I am not sure why you are asking how quickly they would recover your account. This does not matter. It would probably not be minutes but would probably be quick enough so that the escrow would not be able to secure your account.