Yep, been through it lots w/ client's machines & it's not a problem. Swap the Board, install the OS & as the others said, phone MS to Activate. It's true, all you have to do is explain & they'll generate a new product code.
The same OS has stayed w/ the same, original owner/purchaser & in actuality (except for the M/B) still in the same machine as it was. Ergo, still, 1 license, 1 owner, 1 machine... no worries, eh?
Cheers,
Drew