I haven’t actually made up my mind yet. 🙂 He doesn’t have to be an alpha at all. His position is not a public one, after all, and his power is, I think, a very shady sort of power. Also, genetics is only one part of the story. A man with Mycroft’s mind could absolutely make people dance to his tune, if he wanted to.
Yeah, the more I think about it, the more I think I like making him a beta. He’s confident, but not aggressive (except passive-aggressive—and the way he acts with Sherlock doesn’t count; siblings the world over grump and snap at each other). He’s perfectly capable of using threats to get what he wants, but it’s just a tool in his kit, not a natural aspect of his personality. He’s lazy, not competitive (not that an alpha can’t be lazy, but they do tend to have an ambitious drive that moves them forward).
Oh! And, you know, that would explain Mycroft’s love of subtly flashing his power and influence around. I don’t think he’s really an ambitious, competitive man, but I think he REALLY DOES LIKE sort of passive-aggressively sticking it to the snotty alphas of the world.