If I perform a system backup with the Backup and Restore Center in Windows Vista, can I open/restore it in Windows 7?
Nope, it restores the entire image.
But you have tons of options when upgrading from Vista to 7.
Mainly, you can just install 7 over Vista (it says "In Place Upgrade" in the Windows 7 Installer) and it'll keep all your settings and programs anyway.
Or use Windows Easy Transfer if you really want/need to wipe the drive before installing.