The USPS will treat anything that obvious as trash, and not levy a charge. You're better off just returning (blank -- make sure you get rid of anything that IDs you) cards.
Once upon a time, I worked (IT) for a direct marketing company. I've seen brick/cards delivered by the USPS before. Now that was some 15 years ago, but they did deliver it.
Technically it is a properly address and postage paid "package". They may have modified their rules, I don't know.