You are required to remove it from one computer before you use it on another.
While they have no means of knowing if you have removed it from the old drive, they will if you try to use it on 2 computers, because it will neeed to be activated when used on the second computer.
When you try to activate the second system activation will fail and a call to Microsoft will be required in order to activate it, when you tell them you have installed it on another computer you will be asked how many computers it's installed on, as you only have licence for 1 you will say 1 and the new activation code will be issued.
Once that is done the activation on the old one becomes invalid and you will no longer be able to use it, as the OS will become unusable the moment it's connected to the internet.
It's not so much a question of removing it from the old drive, you could leave it on an old drive for a backup in the event your drive died, at which time you could plug it back in. So while it's used on the same hardware it's ok.
You just can't use it on more then one system at a time, Microsoft is pretty good at detecting abuse of licence, a second install will result in one or both being deactivated.