Not as big as you imagine. But then again based on your other posts you are very conservative when it comes to stocking.
". Like most members of the genus, they feed nearly continuously on both micro- and macroalgae. Large adults may reach 22 cm in the wild, but most are half that size."
No. I've seen quite a few very large purple tangs in the hobby. Probably in the 8" range. Much larger than half 22cm. And most of the ones I've seen aren't nearly as aggressive as they are made out to be. Not any more aggressive than most other tangs.
They aren't any more aggressive than others like the Clown tang, which I have found is very aggressive even in a large tank. Purples get Ich easily, so be conservative as your tank isn't long enough IMO.