This is sort of tricky, as I think it may be against the terms of service with Xbox Live.
Technically, yes, the downloads would be on the systems hard drive. So long as the users do not delete the downloads, or keep your profile and can use it to re-download them, there should not be any issue with the downloads. But, if a license issue presents, or the hard drive breaks, or some unforeseen consequences occur, this would not work.
The big issue is that you cannot trade or give your gamertag away. You cannot even give it to friends or family. So this would be a major issue. If you no longer plan to use Xbox products, you probably don't care, but the buyer might. If it's not something you're too worried about, then I guess it would work okay.