It is probably safe in the sense that there will be no harm done to the data on the drive, however it will likely not boot without problems.
Windows OSes are tied to the hardware they are installed on. If you just pull the hard drive out of one machine and install it in another machine, Windows will detect that the hardware has changed and will invalidate the Windows license key that was entered when first installing the OS. You will likely have to call Microsoft to get a new license key.
Will it boot without problems?
It will complain about every missing device and have to install drivers for every new device. By device I’m talking about everything down to chipset level support, on board USB, brand of IDE or SATA controller, etc. If you are switching brands of video cards, or generations, there is a good chance you’ll end up in Safe Mode with a low resolution screen (until you fix it up).
Unless it is an identical or near identical motherboard (which by “new system” I’m guessing it is not), all these changes will probably invoke a WGA reactivation. This may not need involve calling Microsoft, you may be able to do it by typing in the XP license code, assuming you have a retail Windows XP and not an OEM version installed by the manufacturer. Even there you may (or may not) have a chance if you move between like manufacturers, that is, from an HP to an HP or a Dell to a Dell.
If you move (say) from a Dell to an Asus M/B, chances are poor reactivation will be accepted.
That being said, I have had very good luck reactivating my retail copies of XP over several motherboard upgrades, both by moving a system disk or by reinstalling fresh.