It depends entirely on the agent. I don't know if all of them have access to it, but they can sign onto a system that lets them access the airport DM lists, etc. I've been able to have them put me on standby during pre-irregular ops circumstances a few times when I called up to be proactive. On at least one occasion, an RCC agent flat out told me the phone agent had lied and that it wasn't possible (but of course it was possible, and the wonderful phone agent had saved the day for me).

During irregular ops, of course, phone agents can protect you onto other flights, confirm seats, etc.