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I'm not sure, I wouldn't think so.

Refurb products are usually excluded from a lot of promotions. Such as student discounts, the back to school 100$ Mac App store stuff, the free iPod promotions they used to do, etc.
 
Refurb Macs are shipped with the OS that was originally installed. They do not qualify as new purchases.
 
If Apple holds true as they did with Snow Leopard, then yes, certain refurbished machines will qualify for the Lion up to date program.
 
When I bought my refurbished G4 iMac back in 2003 it shipped with OS X 10.2 Jaguar and I qualified for a free (I had to pay for shipping) upgrade to OS X 10.3 Panther through Apple's Up-to-Date Program. So there's a pretty good chance that Lion will be available to those who purchase a refurbished Mac after June 6th. Keep an eye on this page OS X Lion Up-to-Date Program for details on how the free upgrade will work and to see if refurbs will qualify.
 
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