Can you install windows onto an external HDD plugged into another computer?

My GF's lappy is stuffed, XP loads but goes real slow, have to wait about 5 mins before you can do anything.
So i got a copy of XP to format and reinstall, but i cant do it.
I've put the disc in and boot from CD drive and all goes according to plan, but halfway through "windows checking system" or some shit, an error message comes up.

So, Is it possible for me to pull the HDD out of the lappy and plug it into my desktop (i have a caddy to do it), format it and install XP on it.

Then bung it back into the lappy...

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Balls.