Hey Dan,
You bet! Apple transfers the coverage from owner to owner. Really it just follows the unit as you said, but you have to let Apple know. Apple says to allow about 6-8 weeks but I just did one in 2-3 weeks -- payperwork arrived yesterday, transfer initiated first week of this month.
<a href="http://www.apple.com/support/products/proplan.html"<Here is Apple's></a> link. In one of the pdfs (lower left nav bar) is the address you need to send the paperwork to.