From the FAQ page (http://www.iflygps.com/SUPPORT/Frequently-Asked-Questions):
Q: My iFly AP won't power up after not using for awhile?
A: Sorry you are having this problem but all is not lost. Your battery is probably just super dead. Flip the battery switch "off" and plug in the unit, wait a couple minutes, then flip the battery switch back to "on". It should now start charging. Let it sit for several hours, or even overnight. You should be flying now!
So, yes, it sounds like the battery switch must be ON for the battery to charge.