If there are no actual mailboxes at POP, you should be able to leave outgoing mail at the front desk. Be aware that mail sent from WDW can take quite some time to arrive at its destination. I do nt believe the boxes are checked daily. They are not "official" postal service boxes, but are transported to the post office by Disney CMs.
Since we usually have a car, if I have to mail something, I usually just take to the LBV post office. It is a fairly short drive from Disney property. It is located in a shopping center on Vineland Rd, north of WDW.