Yes, you absolutely can! We did this in February. We were already through security when our flight got delayed until the next day. It was easy to pull out my iPad and book a room for that night. We chose a POR Royal Room just for fun. Then we walked back down to ME, showed them the new reservation, and got in line. While in line, we called Magical Express to schedule our return trip for the next morning. They asked us to stop by the front desk of the resort to have our return transportation notice printed out, so we could have it for the bus driver in the morning.
FWIW, I was able to get an AP rate at POR even at that short notice. We got back to Disney in time to grab a quick dinner at the food court then take the boat to DD for more shopping and a sundae at Ghirardelli. For an unexpected travel delay, it ended up being a lot of fun!