We attended HF on Long Island, not sure if all the locations are run the same way but in general you'll have two kinds of interactions with the coaches. Make that three:
There are coaches on the field coaching each team and there are several of them. There will be a lot of discussion about what's happening (maybe even some joking around) between the coaches/players that will be interaction but not specific to that player and being recruited by that school. It's a good way to get to know the coaches a little outside of recruiting and players can pay attention to what sort of personality the coach has.
There are coaches between the fields watching games. I found that they were generally alone or with the other coaches from their school - not in packs of coaches. That's when I saw players approach them to talk. I sat near-by while players lined up to speak with the Macalester HC on one field and then later sat near the Harvard HC while players did the same thing. Most of those discussions were about grades, test scores and what field the player was playing on next - and would the coach be there or could they be there.
Then there were conversations initiated by the coaches after seeing the player - where it was one on one and started by the coach. These were usually off to the side, right after a game and no other schools were around.
There may be other situations but those are the three scenarios that I saw the most while there over 2 days. For the purposes of the player tracking down the coaches and having a discussion with them I think you'll find the opportunity to speak with them alone without other schools around.