Does the warp drive allow to travel between universes? Even in a level 2 multiverse?
Level 1 multiverses almost certainly exist, and any FTL drive would be able to move between them. As far as i know this includes an Alcubierre drive, assuming you could build one. So yes, an Alcuierre drive could move between level 1 universes.
As far as I know the only even remotely plausible realisation of a level 2 multiverse comes from eternal inflation. Your problem here is that the spacetime in between separate universes is expanding exponentially. I don't know what the top speed of an Alcubierre drive is (I assume there must be a top speed) but I'd be surprised if it was high enough to overcome exponential expansion. So I would judge that no, you can't travel between different level 2 universes.