he should be able to restore everything onto the installed new HD by inserting the Leopard install disk (if you can find it) with the backup drive connected and running the TM restore routine. After that, you can upgrade to Leopard without much difficulty, though it may break some applications: search this forum for discussions back when Snow Leopard came out
But since Leopard (10.5) came out in late 2007, there's a good chance you have Tiger (10.4) on the system. I don't know whether (say) the Tiger versions of Pages, Numbers, and Keynote (say) work with Snow Leopard: in any case, Apple tries to get you to buy a box set of OSX + applications if upgrading from Tiger to Snow Leopard
Since Apple offers an upgrade route from Tiger to Snow Leopard, I think it's virtually certain SL will run on your machine, provided you meet the advertised Tech Specs: otherwise, they'd just PO a lot of folk. The caveat is that some hardware has had compatibility problems; I expect much of this has since been fixed with new drivers, but if you upgraded machine hardware since original purchase, it's worth double-checking about hardware
Snow Leopard Breaks Some App Compatibility
http://www.tomshardware.com/news/snow-leopard-mac-osx-compatibility,8556.htmlTechnical Specifications
http://www.apple.com/macosx/specs.html