I can confirm...I have done this stand-by switch (from EWR to LGA). Also works for LAX/SNA....those are the only two pairs I can confirm....

As for luggage it depends on the situation. If there are plenty of seats when you check in you should be able to confirm the stand-by then and have no problem checking bags through. If you end up having to stand-by at the gate I wouldn't do it with anything but a carry-on. It can be done but they don't guarantee your luggage goes with you.