No 32bit and 64bit are not compatable to upgrade, you would have to buy a new copy of 64bit and do a fresh install.
A genuine Dell w7 disk would work, but getting one from eBay is a gamble, they can be selling you anything.Just got a 6 month old Dell Optiplex 7010 with 32 bit W7 Pro. Want to go to 64 bit. Can I just buy a $10 OEM Dell W7 Pro 64 bit restore disc on Ebay?
you would have to buy a new copy of 64bit and do a fresh install.
To answer your question, yes you could buy that disc but you can also download the iso for the version you have a license for by following this http://www.sevenforums.com/tutorials/1649-clean-install-windows-7-a.html