The word deactivate can be a bit misleading. All this does is remove the product key from the PC so that the Windows installed on the PC is no longer be activated with that product key.
If you get an upgrade copy of Windows 7 Ultimate instead of a full copy, then you will not legally be able to use the Windows 7 Home Premium since you are replacing it with the upgrade to Ultimate as per the EULA.
If the Windows 7 Home Premium is an OEM copy instead of retail, then you wouldn't be able to use it's product key to activate on any other PC since it's permanently tied to the motherboard of the PC it was first activated on.
If the Windows 7 Home Premium is a full retail copy, then yes you will be able to install and activate it on any other computer you like so long as it's not installed and activated on any other computer. If it doesn't activate online as usual, then you could activate by phone instead.
Hope this helps,