Scheduled startup/wake while on battery power
No, you can not schedule your Mac to power on when it is battery powered.

Design Choice &amp; Deliberate Limitation

A scheduled power on event requires the Mac be connected to mains power. This is a deliberate limitation enforced by Apple's engineers. This is to protect your Mac from powering on while in confined or poorly ventilated spaces such as in luggage. In these situations your Mac risks overheating and being damaged.

Being able to power on while on battery is a common feature request to my Power Manager software. Sadly it is not possible without risking damage.