Justin, in this case everything should work correctly also. Users will be logged into their own area and have access only to their data without any conflicts.
There can be possible conflict in using feedback module on both sites, for example. If there is a limit setup for using feedback it will not allow send two feedbacks one by one within 30 minutes from one IP address. This is default restrictions and can be redefined in /SB_ROOT/config file:
[feedback]
limit_for_next_send_message = TIME (in minutes)
Hope this answers the question.