It totally depends on how the ad is part of the team.
I have worked on shows where the AD is just there to get coffee, get sandwhich, pick up dry cleaning, etc. Other times, the AD is more like a second director. Currently, I work at a theater witha resident AD, who works along side the director, handles text changes, takes blocking for u/s rehearsals and possible remount, offers suggestions to the director, directs the u/s cast and maintains the show artistically during the run. It's great - I love have someone else during the run to help maintain it. It rarely gets in my way or make my job harder, unless the AD starts to try to do my job.
I often feel that you kind of feel out of the relaitonship as you go along, observe how the AD is used by the Director; but also feel free to ask up front how the director works with an Assistant.
(I have also worked as an Assistant Director, and I had very little interaction with the SM, other then during tech, I would go off with the SM and give calling notes - but mostly that was because of my SM experience, and this was a novice SM)
In the end, the AD is just another member of the team, like the Dramaturg, Choreographer, Fight Director, Music Director, etc, etc, that you juggle and work with - my big note is to work out that relationship with the AD up front.