You will not be able to participate if you join after it starts. In all iterations of AQ, you cannot join a map that started before you got there. Since the is one map, you will not be able to join at any point after the fact.
The rewards suck anyway
I wish they would figure something out with this new AQ lineup. Its making it even tougher to recruit as its always something holding or waiting between they will swap.
Guy waited to collect raids, but now was locked into coliseum being pushed back to Monday and now likely won't be able to help AQ rampant. These little tedious things are what makings recruiting a pain the arse, if you're lucky enough to find someone these days.