Are you talking about running RAdmin and VNC (for example) on the same computer at the same time? If so, that's totally doable.
I have several clients' computers that have multiple remote access programs on them. As long as they're listening on different ports, they will all get along nicely. I've even run 2 different versions of RAdmin server on the same machine - v2.2 listening on port 4900, and v3.x listening on 4899!
Actually, Radmin could conflict with another remote control software, especially if this software uses mirror driver technology aswell. But nothing "bad" could happens, at maximum sone or both remote controls will fail until you remove a second one.
Good point, Eugene. I had forgotten to account for the Mirror Driver; I can see where that could cause issues.
In fact, I encountered a Mirror Driver conflict not that long ago; I believe it was with the RDP based remote control built into Microsoft's beta Live Mesh software. I didn't care much for that aspect of Live Mesh (it was VERY slow), so I disabled it and all was well.