This all depends on additional factors of your network configuration. Moving a user from VLAN 10 port to VLAN 1 port would work if you have a routed interface setup on the network tied to VLAN 1, and also VLAN 1 is egressed / trunked from the switch to the router and back from the router to the switch. Seeing it's a different broadcast domain they are connecting to, you would need to also have DHCP setup for that scope being used.
If you walked into one of our buildings and you plugged into port 3 and it was on vlan 10 and then you plugged into a different port and that was on vlan1, other than the fact NAC would stop you, it wouldn't work because of how things are setup on the backend. As Ryan mentioned, there are several variables that would allow this to work or not work. It all depends on your individual config.