If the transmitter drew 200mA. then you would have more than a few hours out of a charge, at least 8 and maybe closer to 10 hours
On the bench I ran a test with a freshly charged 2000mAh 3S lipo with two silicon diodes in the positive lead.
With a 72Mhz module the 9C is rated at 280Ma draw, but with the TM-8 FASST module it is less than 200. The 2000mAh lipo ran 12 hours on the bench (intermittent runs of 3 or 4 hours) so even a frequent flier will not have to charge their radio after a few hours of use with either Eneloops or a lipo properly set up with diodes for voltage reduction (they don't regulate) The lipo ran from a high voltage of 11V (transmitter indication) to low voltage warning where the lipo was still at a safe level.
The Eneloops are a very good choice for a transmitter due to the very low self discharge rate.
Pete