Is it acceptable to put conduit or flex through the wall directly
to the back of the buzzer?

Sure. As long as it's a weatherproof box, and the buzzer can be removed
from the front to allow access to the splices.


BTW I heard a discussion in an inspector meeting that a normal 3R box outside
an exterior wall was a wet location and you couldn't run Romex into it.
It was far from a unanimous opinion but inspectors can be quirky guys so don't
be surprised if you hear this again.

Vote me for "this is BS".