When you perform a backup this only saves files, such as the ones you would have in your documents folder, such as word files, photos, music etc.
It does not perform a backup of installed software
when you format the hard drive and install ultimate, you will be able to restore your personal files, such as photos & music
But you will need to install all of your software again from scratch.
If you want to keep your files and programs, you could try using the upgrade option, rather than formatting the hard drive and doing a fresh install
personally I am not a fan of the upgrade option, and would advise saving all your personal files, then installing a fresh copy of ultimate, then install all your software
I know this takes a long time, but your system will run a lot better than using the upgrade option, as this can(in my experience) sometimes cause system issues.