A device without a battery is basically a "dead battery" device, and the charging spec's dead-battery provision (DBP) says:
PD (portable device) shall not use the DBP current to perform unrelated tasks, such as:
Charging beyond the Weak Battery Threshold
Making a phone call
Playing a song, video or game
Establishing a wireless connection
Only devices that can operate stand-alone from internal battery power are allowed to use the
DBP.
So I think using a charging port is not an option.
The spec defines a dedicated charging port (DCP), which resides on a charging device that provides power but doesn’t enumerate the attached device. But that is not what you have with a hub port.
What if you tried creating a compound device with a hub, and two downstream devices: your device and a USB 3.0 device that functions as a power supply and uses a vendor-defined connection to provide power to your device (generic HID would be one option).
The USB 3.0 device can draw > 150 mA only after it enumerates so your device would need to able to enumerate using < 150 mA in case the power isn't available yet. Maybe you could emulate detach and reattach when power becomes available, but at least one method for doing so is currently patented. Instructing the hub to delay enumerating one of the ports until the other port is enumerated might be feasible in theory but doesn't sound easy to implement, could require a hub filter driver.
Again these are my initial thoughts and I may have missed something.