Can the eLite can be charged via 12VDC while in operation?

Yes, it can be, however once you go over the wattage that the charger is producing it will shut off the charging feature. For example, the solar charge controller can produce up to 100W. If you stay at a speed where the output is less than 100W (i.e. 1/5 of total power output) it will slowly charge. Once you go over 100W, the charger will stop charging until you back off the throttle to less than 100W output.