If it's their first time flying, I'd advise even more strongly for sorting this out in advance. You have to do stand-by at the airport which might have you there several hours early to arrange. Those open seats are probably a mix of unsold and unassigned so there's no easy way to tell really how full the flight is, plus you have the Northeast weather to factor in. It's been a rough winter already and probably still will be rough in 2 weeks. One cancelled flight the day before and that nonstop is now sold out.

If you were flying solo or with one other adult I'd say go for it but IMHO you're just inviting problems by tring for standby with a big group, the least of which will be extra time and discussion in the airport before taking the connecting flight you're already booked on.