Not all that much hassle to wipe the whole HD with DBAN and you’ll get a lot more for a fully working computer with a HD even if it’s wiped if you can’t be bothered reinstalling Windows – no cost to the buyer to choose their flavour of Linux. Better ways to keep backup than on an old HD which never gets spun up.
Oh and to the OP, yes it will kill viruses and anything else that’s alive on the disc. Not too much hassle to reinstall Windows from discs which came with the computer, though if you’re doing it that way rather than with a recovery partition then you or the buyer would probably still need to reinstall drivers etc. TBH if that’s what you’ve got then personally I’d just wipe the whole disc, not bother reinstalling and sell it with the discs (describe it honestly like that and you won’t put off many potential buyers).