All passengers on the same confirmation number are checked in together so if you put everyone on the same reservation you'll check in altogether and should get sequential boarding positions or at least positions that are very close to each other. Check in is available 24 hours prior to departure, 24 hours prior in the time zone of departure. So if the flight departs from the eastern time zone at 3pm, people living in the central time zones can check-in at 2pm.
To ease your mind about check-in you may want to consider purchasing EarlyBird Check-In which completes the check-in process for you automatically and assigns you a boarding position ahead of non A-List people who did not purchase EarlyBird Check-In.
My recent experience was that the parties with the same confirmation number were checked in simultaneously but were NOT given sequential numbers. 2 groups of 2 = 4 people on 2 confirmation numbers. No EBCI. 3 were together in the A group and my youngest 15 y/o niece was in the late B group. I would not have believed it if my sister hadn’t sent me screen shots. It happened with all connections on a RT so 4 flights. I had to go back and make sure I didn’t buy EBCI for 3 but not 4. I can’t post the screen shots without showing their names so I cannot show you the proof (no photo editing tricks known by me).
Fortunately they were able to save a seat but I was really surprised. Just not her day, and of course, endless teasing by her 2 older sisters.