Short answer, no.

A game that's an ArenaFPS focuses mostly on fast movement, and quick control. Movement being how the player can dodge, and get around the map, fast. And control is how a player controls a section of a map, which could be item control, weapon control, or just position, though there’s more to this that I’ll get into.

In halo, movement is not fast, and there are times where you're camping (waiting for someone to pop out, kind of like in counterstrike). While controlling a section of a map can be a thing in a normal FPS, in an ArenaFPS, you can’t just sit around and camp. You must always be chasing something, items (deny the other player), weapons (deny the other player), or the other players them-self.

I’m sure there’s other aspects I’m missing, but this is the basic idea on what makes an ArenaFPS. :)