Is it more efficient to run your boat with the main engine pulled out of the water when using the TM, or does leaving it in do better? In my particulat case I have a 14' aluminum Lund, a 20hp Honda, and MinnKota 55lb PowerDrive (bow mount). I was just wondering if pushing the stern further into the water by bringing the motor out gave less or more drag than the shaft being in the water?

I fish a 16' aluminum.  I keep the main motor down to help keep the back end from blowing around in the wind.  If the wind is very strong I add a drift bucket.  That 55 lb trolling motor should pull your rig around all day with out any problem.  

Try it both ways and see how it works for you.

I was just curious if you'd get more battery life on it

I think you will find that minute amount of drag would have little affect.  However running without the motor in the water will probably make you use more battery because you will be fighting the boats position a whole lot more because you don't have the motor in the water to keep the rear of the boat from going all over the place.

I agree with way2slow.  The additional drag of the big motor is minimal when estimating battery life on the TM battery.

I keep my outboard down a vast majority of time, I think it helps stabilize the boat, somewhat acting as a rudder.  You'll especially notice a difference in any amount of wind.