Yes, that is very well possible.
But an external isn't really suitable for "preserving" data. They fail too often. But it's nice for an extra backup and to copy data somewhere else.
I am replacing and old computer that had a celeron 1100 prosessor with a HP Compaq 7800 that is used and has had the operating system removed which I will replace with my XP Home OS.I recently had the hard drive in the old unit cloned from the original 20 HDD to a 250 IDE hard drive which now has 94% space remaining in it, can I install that hard drive into an external hard drive to preserve my old data? The new computer is a SATA drive.