|No it will not work because the recovery wizard needs to take possession of the whole hard disk in order to restore it to factory condition.|
Any time you create a partition, HP recovery will cease to work. This is because the recovery wizard is aware of the original hard disk geometry, so any change made to it triggers the wizard to stop working permanently.
You really need to backup what is dear to you. Don't you have DVD burner? Or why cannot you get a portable hard drive?