Alias iCloud email as Apple ID?

With the new updated feature of using @me.com and @icloud.com emails as Apple IDs, I would like to know if it is possible to use an alias iCloud email instead the old (outlook.com) Apple ID, even if the primary iCloud email address is different than the alias.

Some plain explaining:

• aa#aa@outlook..#com --- my current Apple ID, that has to go away
• aa#aa@icloud..#com --- is primary iCloud email address (I can log in with that too, before the change)
• a###a@icloud..#com --- my alias email address, that I wish to be the new primary iCloud email address and my Apple ID