I am by no means an electronics guru and have nothing to back up my findings except experience, but I have run a Raspberry Pi3 for a minimum of 30 minutes with a 3.7v 500mAh Li-Po battery connected +to Pin1 and -to pin9. I have done this to record video while running a Lighttpd server to serve the video over the Internet. It seemed to function fine.
What will cause the Pi to fail is a mystery to me, but I own about 7 Pi's, so I am not concerned with a hardware failure.
My camera is hooked up to a servo to "look" higher and lower, I have NOT tested the servo while running the PI on the 3.7v Li-Po battery. This seems like it could pose a power supply problem. With my servo drawing 5v power from Pin4 (grounding to Pin6 and control at Pin12 [GPIO18]) then I would be relying on the Raspberry Pi3 to convert the voltage from 3.7v to 5.0v - that seemed like TOO MUCH to ask of it. I don't know why, but since I don't use 3.3v, I just think it's an "internal" voltage that they give us access to for reasons I have yet to explore.
I think the RAM, Processor, camera, and other "internals" can handle 3.3v or 3.7v just fine. I think the other "stuff" on the "board" itself is NOT designed to jump voltage UP so as to power 5v peripherals. Even low-power 5v LED's seem dangerous to me and and I am not willing to sacrifice a Pi to find out if I can "blink an LED" or move the Camera.
All I'm saying is that I HAVE had success running the Raspberry Pi3 model B V1.2 at 3.3 volts (I have NOT tried this on a Pi2 or any other version), but I don't think it is wise to try to use the GPIO pins if you do this.