Is this possible?

If I unlocked the teams, would I be able to allow only certain players this option? Say for example, all players can ally/unally all but one certain player from the "allies" menu. Would this be possible, if so how?

Well, one option would be to use a trigger based alliance system. You should be familar with them - the "-unally red" kind of system, it gives you complete control over which alliances are allowed, and which are not.