I think you can yes, not entirely sure where from though.
Well it depends really, are they still stained or is the fabric looking faded?
If it's the former then you should have no problem at all, as the wet vac forces water plus cleaner into the fabric agitating the stain, then sucking up the loose dirt, where as applying a cleaner by cloth with take away the top surface of dirt but wont get right down into the fabric to remove the entire stain.
It's certainly worth a shot, depending on the price of rental etc