Not a pro here. But No.
You cannot install onto a HD with one pc, and then use the HD on another PC. When XP installs it uses the specific PC configurations and sets them up on the HD. hose configs are not the same as on another pc.
If you have files on the car pc HD that you need, I recommend you install that HD with the original (home) pc HD...run both. Transfer the wanted files from the pc HD to your home PC. Then redo the car pc. When done, you can transfer the files back onto your pc HD.
Hope that helps.