Great idea! The free upgrade should work, it should just see what version of Windows 8 you're using and upgrade it.
I've looked to see if there is anything about Windows 8 Pro upgrade difficulties and can't find anything.
Updating to Windows 8.1 from Windows 8 - Microsoft Windows
I'm updating Windows 8 Pro right now to Windows Pro 8.1
However this is a version I've had since the upgrade from Windows 7.