Ultimately, the answer to this question varies on the agent checking you in. Due to the generosity of various gate agents, I have arrived at the airport for an earlier flight, been put on it, and then upgraded even though I was ticketed to go out on a later flight. This usually happens only when either the earlier flight is fairly open, my current flight is overbooked in coach, or there are no upgrades available. Usually, if I am told there are no upgrades available, then I ask the agent if he/she can put me on another flight in F/C. Usually they'll do it if the flights are open. These are on non-refundable tickets too.

Regards,
RChavez