Will downloaded Windows 7 backup disk do a clean install?

Yes you can use the Home Premium Product Key on COA sticker shown above to Clean Reinstall - Factory OEM Windows 7.

I would use Home Premium unless you know for sure you need one or more of the extra features in Pro because otherwise it is the same exact OS: Compare Windows 7 Editions - Windows 7 Forums

But if you know you want Pro for sure then you'll be abandoning the Home Premium which came with that PC and it will go to waste. If so you can indeed boot the Pro Disk to Delete all partitions to create and format new using the Drive Options pictured in Steps 7 and 8 of Clean Install Windows 7. The Upgrade disk will still allow use of Upgrade key during install since it sees the underlying OS when it is booted.

You don't need to worry about asking back as many questions as you want. That's what we're here for. But you will do yourself immense good if you study and follow the steps in Clean Reinstall - Factory OEM Windows 7 which compiles everything that works best to get and keep a perfect Win7 install.