Does Alistair Leave Your Party?

Alistair only leaves the party if you recruit Loghain. Alistair only makes a cameo appearance in Awakenings (right at the very start of it).

What happens if Alistair becomes king?

If Alistair is made king, the Warden made queen, Anora will refuse to renounce her claims to the throne, so Alistair orders her to be locked up and only if Alistair dies from the Blight, will she become Queen. ... Furthermore, Loghain will always die if the female human noble Warden becomes Alistair's queen.

What happens to Alistair if he leaves?

If Alistair became the sole King of Ferelden he will still offer to make the ultimate sacrifice calling it "His first and last act as King". If King Alistair dies, Anora will become the new Queen and in her speech will mention that the Theirin bloodline died with Alistair.