Just throwing my two cents in, even though it's starting to sound like a parrot chorus...
I think it can work, especially if one of those AP champs is bot. Even if you end up with 3 AP top, it CAN work if you have 2 AP carries (Cass, Brand, Ziggs, Ahri etc.) and an AP tank, along with a major AD threat (Jax, Vayne, Ezreal, etc.) Sending 3 AP carries top is probably not a good idea, mainly because AP carries don't scale as well with items as other champions. Your 4th top champ either has to be an AD threat (so you have no tank) or a tank (so they stack MR and you lose, badly).
People complain about AP carry itemization on Crystal Scar, but the game was purposefully designed this way. The reason the mid lane AP carry is dominant in SR is because AP carries scale best with LEVELS, and you'll never get a big experience advantage on Crystal Scar.