Can a station be programmed to immediately call another station or outside number when going off hook?
How would I go about that?

You create a hot line...as soon as the phone goes off hook it calls a speed dial number or
station. You have to add the station to the hot line/warm line table set the value to hot and then set the idle line selection to be a feature on a button (such as a speed dial number) or to call a station. This is done in pgm 122. and can be found on page 1-155 (pdf page 169) of the current documentation.

I was told another way of achieving this would be to assign a COS level 2 to the station and type the authorized telephone number in tables under "Allow A".