I wouldn't buy the MP for that short of a day.
You can still get traditional FPs by walking to the machines for whatever you want. My opinion: When the FPs are hours apart and not minutes like early in the day, walking to the machines in the course of touring is less of a time sink. Unless it's a busy day, there should still be quite a lot of FPs at 3:00 in afternoon. Example: sitting here checking the app at 3:05 on a busy Sunday Memorial Day weekend: Haunted Mansion has a 4:05 FP, Big Thunder has a 4:55 FP, Roger Rabbit 4:30. Small World is almost immediate at 3:20! Everything in DL still had a FP although Space was 10:25.
If I knew I had a 3:00 arrival, I'd check the app when I arrived and send someone to Big Thunder for a Fastpass maybe an hour in the future, then grab a snack, ride the Mark Twain, ride Pirates of the Caribbean. Or get a Small World FP and pick off the shorter few lines in Fantasyland or Tomorrowland. Whether it's FP or MP I would get the closest time for anything you want to ride so you can get more later.
Ultimately you have to decide whether getting 3-4 FPs for (probably not headliner) rides is worth the money. If you only a have 2 full days after your arrival day it might help you knock out some of the ones I listed above, but every hour later in the day the FPs also get farther out. So by the time your 4:00 Haunted Mansion can be redeemed and you can get another, now Big Thunder is at 6:30. Then at 6:30, the next one you want is at 9:30, etc. ... and you're all tired from traveling.
PHXscuba