The simple answer is [b]NO![/b]
But on the up side any copy of XP that is the same version will work with your Product Key. As you have Home there should also be a [b]COA[/b] on the side of the case with the Windows Product Key although I find them hard to read there should be one there. If the [b]Certificate Of Authenticity[/b] isn't on the case I would suspect a Pirate installation as a Volume License isn't available for the Home edition.
But you can Beg, Borrow, Steal a XP Home CD and use that to perform a reinstall from or if you are really eager you can create a slipstream install CD though in most cases this is only used to install the OS and necessary drivers for the existing hardware.
There is one other possibility here if you have a IBM, Dell, HP or something similar you may have received the restore CD but just not know about it on several of these systems the Recovery Windows Copy and drivers for the hardware came on a Hidden Partition on the HDD that you generally can not see when Windows is working. If this is the case you can make a slipstreamed copy from that but you have to know exactly what it is you are doing and be very careful.
If you have an off the shelf system you can always buy replacement Restore CD's from the maker by ringing them and quoting the model and serial number of the computer and they will sell you a replacement Restore CD Set.
Col