i was just wondering suppose i was using DC (from here) and went to the post office and mailed

the book but forgot to tell PBS I mailed the book would i still get credited when the post office scans the book?

No.

You would need to contact the receiver and ask that they mark the book received to get a credit. The DC Quick Credit will only be triggered on an active transaction in the system.

Also--if you don't mark the book mailed by the deadline and the book is not a wishlist book, the request will automatically roll over to next book in the FIFO line.  So, I'd PM the requestor as soon as possible to let them know that your copy is on the way.  That way they can cancel their request and avoid having the additional problems/confusion of getting two copies of the same book in the mail.  (If they do get a second copy--per PBS rules they don't have to mark your copy as received.)