You can, but eucalyptus can get overpowering over time. The supermarkets sell a water soluble eucalyptus oil - add 1 only teaspoonful to the RINSE water. There is also a lavender version that can be used the same way.
Another method is to keep a small face washer or similar with a few drops of oil on it. Put this in the dryer with your clothes.
Quite frankly, I wouldn't bother if line drying clothes. I would only consider this if using a tumble dryer all the time.
EDIT: too much oil will rot the seals on the washing machine.
I have a washer / dryer mixed machine. Will the oil still mess with the seals? If so I'll stick to the scent booster that CEO suggested above. Or get the soluble one.