If their present machine had the DameWare console installed on it, it would be possible If they had the ability to view / control your screen, and you were remotely connected to the new machine in another window, would that work for you as well?
These are end-user machines; none of them have Dameware console installed on it. If they did have Dameware they could just connect from their present machine to the new PC directly.
I'm seeking a way to circumnavigate me, as the PC tech, asking the end-user for their password in order to fully set up their new PC. As I said, we currently use VNC to do it but I would like to investigate ways to take VNC off the boxes entirely.
Just RDP to it as usual, then run:
tscon %sessionname% /dest:console
That will disconnect the RDP session and show the user's session on the physical console. I've done this before, when when pre-profiling laptops for remote users.