If you activate the same Product Key twice in one day you will probably trigger over the phone activation, this is a quick process involving you talking to a robot.
If you have the older Win 7 install for a while you should have no issues.
Is the Home Premium a Retail license? If not, you can't use it elsewhere. But you can install Pro over the top.
EDIT: You may be able to perform an AnyTime Upgrade actually - just do a search for it in the Start Menu search box. You basically put in the new Product Key and Windows activates the extra features.
I am not 100% sure if they Product Key is updated or not, though. But I would have thought it possible to reuse Premium elsewhere [as long as it is not OEM]