I think this is a great idea, and we should all do it.
The Post Office MUST hold any mail that arrives care of General Delivery for 30 days.
They can not arbitrarily make a determination that the person exists or does not exist.
So they will have to hold each of these pieces of mail for at least 30 days from each postmark. So in that sense, it will be as useful to send a couple of cards spread out a week apart, thus continuing this 30 day period.
IF there is a return address the PO MUST return the undelivered mail to the sender, marked as undelivered.
If there is NO return address, the mail will go to the "Dead Letter Office" where typically, enveloped mail, with no visible return address, is opened and searched inside for a possible return address, which if found is used to send the piece of mail back to its original sender. Barring finding an address through this process I am then not sure what happens to that mail, ie, whether it is at that point the mail is destroyed or whether it still must be held for some period of time.
In this vein, often local PO's will have to deal with letters addressed to "Santa Claus", and I believe they have some ruling that allows them to amass and hand-off that sort of mail to a single designated recipient.
So in the end, they may have to collect these nonreturnable pieces of mail, and hand them off to Focus Films, if a newsworthy story gets out over this, and/or Focus Films is made aware of it.
Just some thoughts to consider.
It's a good idea, and I'm gong to send a Post Card a week for several weeks.
Jack in Maine