How do you get external power in this aircraft?  I click on the "external power" switch in the cockpit, and check the meter above in ext pwr position, and nothing.  

Right now it is nothing more than a switch that turns on a White Annunciator light.  Has been reported to Carenado for a wish list

If you turn that switch on, will it keep the batteries charged while doing the preflight checklists, or will the batteries die during the prescribed FSX battery drain time?

It will drain the battery. The ext. power switch does nothing more than turning on the annunciator. Also when you put the volt meter to ext power, it's showing "0"