While most malware infections do not affect recovery partitions, there are some which can and it will not matter whether the partition itself is invisible or not.
If you have made a disk image
with an imaging tool
(i.e. Acronis True Image, Drive Image, Ghost, Macrium Reflect, etc.
) or, if using Windows 7, Created a System Image Backup before
your system was infected, then using it is another option. Disk Imaging allows you to take a complete snapshot
(image) of your hard disk which can be used for system recovery in case of a hard disk disaster or malware resistant to disinfection. The image is an exact, byte-by-byte copy of an entire hard drive (partition or logical disk) which can be used to restore your system at a later time to the exact same state the system was when you imaged the disk or partition. Essentially, it will restore the computer to the state it was in when the image was made
. You will then have to reinstall all programs that you added afterwards. This includes all security updates and patches from Microsoft.
It is a safer practice to create the system image on a removable external hard drive, which can be disconnected and placed in a safe area for use when needed. CDs and DVDs are not as reliable as they can more easily be misplaced/lost, damaged or may not work if the CD/DVD-ROM drive does not function properly when you need it.
My wife, uses a similar HP setup as you describe and although we have restore disks, if needed, I would use the System Image Backup as my first choice. Same with my daughter's HP...we use the Windows 7 System Image Backup on an external hard drive which I keep for her in more office.