This gets asked a lot and the answer is the same: not ideal, but it will work. A sealed sub would be better when placing it inside another box basically, so the SB1000 might be a slightly better choice. The PB1000 is at least front ported though, so you may be able to get away with it.
A door will basically pass very little sound

Acoustically transparent cloth will allow the sound to pass through, but the sub is still sitting inside another box, which WILL affect the sound to some degree no matter what.