I wouldn't count on that. I once put a postcard into an official mailbox outside a post office in FTE (Argentina). Something was amiss and I checked the mailbox to find a poor design and a loose lock, and stacks of postcards inside (and international rates in Argentina are very very high).

That said, I mailed from the J.W. Marriott in BKK a few years ago (staff actually took new stamps and put on on the card) and they actually reached the receipients. Did the same thing (but not see the cards beign stamped) at the Conrad a year later and of course nothing ever reached the destinations.