In theory, yes. Skins are tied to player names, so sending a random name out of Red_Player_1, Red_Player_2, etc would be possible. The issue is almost completely down to cost and practicality.
Each skin is its own premium account. There are various screenshots floating around on the forum of Red_Player and Blue_Player in SMP, and you can use /who Red_Player and get real information. Apparently there are nine TF2 classes, which would mean 18 skins for both teams. That works out to about £325 to buy eighteen accounts.
It might be a nice luxury, but for £325 it's just not practical.