I have done same day standby a few times on connecting flights. You are standby for ALL legs. This bit me once where I wasn't able to clear on a connection in DEN (ironically) but was only stuck for an hour or so. I'm not aware of anything in the policy that states you can't change the flight type, but would love additional clarification if there is specific language about that. As with anything, there's also a real chance the gate agent may use their discretion (positively or negatively for you).

Personally I think it could be a bold move to try to standby connect with more than 1 person. Not to say it wouldn't be viable given routes/timing/alternatives etc. but I'd certainly have a pause before making that jump!