Longer answer..... be ready for things that don't go quite as you hope..... your motherboard should auto detect the old drive and you may have to tweak things here and there later...
The new box will perhaps have a different videocard?... If so you will need to delete the old drivers and going round via the generic driver set up new drivers for that.
You might find your printer being silly too because a few years ago motherboards recognised only LPT1 - full stop.
Otherwise a splendid idea which will temporarily save you the cost of a new HDD