Or more importantly not within the EULA that the user agrees to when they first Open Windows.
With Activations when you make 3 changes to the Hardware you need to reactivate the Software and if this happens a lot for instance with a Test Machine that you test new Hardware on you will run into problems with Reactivation. Remember a change is also returning the system to Original Condition after testing a new Video Card, So fitting the Video Card is 1 Change and refitting the original Video Card is another change.
Fitting 6 new SCSI HDD under XP resulted in a visit from M$ Legal who was convinced that i was Pirating their Software so in answer to your question Yes M$ do track their Software and Activations.
But probably much more importantly will his 4 year old system actually run 7? Have you checked it with the Windows 7 Upgrade Adviser?
http://www.microsoft.com/downloads/en/details.aspx?FamilyID=1b544e90-7659-4bd9-9e51-2497c146af15
Seems fairly pointless to buy a copy of 7 if it's not going to run on the existing hardware. ;)
However if he's purchasing a new PC in a year or so unless he has some White Box Shop to sell him a Bare Metal computer they all come with a Windows OS installed so when he buys that new computer in a year or so time it will come with 7 preloaded.
Col