Pro Mini VIN Problems / can I use LI-ON 4s pack ?

OK yeah looking at heat output and things i guess its jsut not going to be worth running the regulator. That brings me to the other half of the question can i run the pro mini at 2.8V - 4.3V ? by using 1 cell in a 4 cell pack in series with a cell balance board? or would one cell drain too fast ? (the device only gets turned on every few minutes for about 5-10 minutes with usually at least a few minutes break)