The easy answer is that transformers are passive devices, and have no effect on battery life.
As to the sound, I've got switchable output transformers in my Littlebox. I ran the LB without trafos for a couple years, then got it upgraded to includes them. My general impression is that I like the sound with them better, and I always run with them engaged.
Unfortunately though, I've never tried to do any kind of comparison with or without them. The only thing I could really do is do one set with them engaged and another set of the same band on the same night without them engaged, but I haven't even done that.