Mm, I always wondered about that (not least every time I re-watch one of my favourite actors in Scent of a Woman).

The hurrah/huzza derivation seems a pretty likely one, doesn’t it? The OED has a 1682 cite for huzza, and this most appositely from Farquhar’s The Recruiting Officer in 1706:

Huzza then! huzza for the queen, and the honour of Shropshire!