This is always iffy. There are a few possible outcomes to this scenario and only one will actually happen:

1. Bag gets to EWR, remains overnight and boards the next flight to ITH. Agent is right and the bag waits at ITH for pick up.
2. Bag gets to EWR, remains overnight and never gets loaded on a flight because the baggage handlers aren't sure what to do with it since it's tagged for a cancelled flight to ITH. This isn't likely but possible.
3. Bag gets to EWR, remains overnight and then gets boarded to SYR with your daughter. This is possible if the bag scanner gives the baggage handler an alert that the passenger was rebooked via SYR. In this situation the bag tag will be manually updated to SYR and it will arrive on the flight with your daughter. This one is just as likely as #1 IMO.

In my experience you just never know. The other problem is that the bag tag ID you get in SFO will be useless for tracking in many scenarios. Someone at EWR will likely re-tag the bag which generates a new baggage ID number. This doesn't always show up in the mobile app as the current bag ID so you can't track the bag. And if you can't track the bag then the baggage service center is going to have a hard time as well.

My suggestion, if it's not too late, is to short check the bag to EWR and have your daughter pick it up there. Then she can check it in with whatever flight she winds up on the next day. Maybe a seat opens to ITH and she can get on that flight. Always possible.

-RM