I think my biggest concern if I hadn't interacted at all would be that it shows a lack of interest. I am also a full time student and work like all the time and I managed to attend webinar session for aads. I interacted with the admissions reps they had representing them. Also, they had a lot of options and availability. But they probably don't look into it to much. I will say I think my interactions aided my application, I felt good about them. They had some specific degree sessions, like for the MAR. I attended that one.
Right now, if I get in HDS or YDS it will impact my choice, but all these cities are so expensive to live in, lol, Nashville is prob just as expensive as boston and new haven.