Really depends on the GA, but officially, I think the answer is no.

That said, if the ORD-SFO plane is oversold by 50 and ORD-OAK is empty, of course they'll throw you on the OAK flight.

I've tried to do this before with ORD-LAX/SNA. Have had success a few times; others, I've been told that I have to go where I hold a ticket.

Basically, you have to find somebody who looks very pleasant and show them your best charm. (Also helps to not have checked luggage.)