What I want is a button on a gui which can be clicked even when a dialog is being run.
Anybody know if this is possible while still using the dialog system?
I doubt it. As it is the dialog system pauses everything else in the game so every button and action will be disabled. If your programming skills are high enough you could try and script your own dialog system. I did that once when I had a similiar problem. Apart from that I can't really come up with any solution.