[Jenda_]

Yes, with a step-up converter to 3.3V.

Unfortunately it has no sleep mode (the supported power-down modes erase the main RAM, leaving only 64KiB region, so it's unusable for suspending of the booted-up Linux), so it will last a few hours at most.

This is a common problem with almost all of such boards. And we see great power management is definitely possible: Android phones can suspend to milliwatts for a decade. But there is no support in this hardware, where you can run "normal" Linux, not Android :(