That is correct, as long as they are listed on the reservation they can check in, even if they are not "the lead name". Whoever checks in first can take all the ID cards (the keys) or they can take just theirs and leave the rest at the front desk for the other half of the group to pick up when they arrive. If you are not planning to meet up right away, leaving them for the other half to pick up is a good plan, that way the group that gets there first can go do something and not have to worry about the other half being locked out.
One thing to keep in mind though is that any remaining balance due on the room (if it is not paid in full) is required at check in, so whoever arrives first will have to take care of that.