On most lights… no. As SammysHP said, moon generally requires the MCU to be awake, so it would be the same as just leaving the light on normally, in moon mode. You can do that if you want, but it’ll drain the battery like 15 to 20 (edit: 50) times faster than low aux.
Power use varies, but a typical amount (edit: for a FET+1 driver) would be about 1.7 mA… of which like 1.6 mA is used by the MCU and any other active components of the driver, and only ~0.1 mA is used by the LEDs.
On some newer MCUs with DAC-based avr32dd drivers (like D3AA and Hank’s Lume X), it might be possible to run the DAC during standby mode… but the details aren’t known yet. At a guess, if it works, (edit: and with a power circuit designed for this) it might be able to do a moon level at perhaps 0.5 mA. Setting the hardware registers the right way might thus enable a significantly better “standby moon”, as compared to the regular “ramping-mode moon”. But the power use is still a bit high.
The aux LEDs typically use about 0.1 mA on lights which implemented them well. This works out to about 1 year of illuminated standby per 1000 mAh of battery capacity.
The new dimmable aux LEDs raise the minimum power to about 0.3 mA. That’s part of why I’m not very enthusiastic about them. It uses more power, and makes them strobey.
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Edit: Nevermind, these drivers can’t do a lower moon after all. I measured moon at 3.7 mA on a D4K-lume and 5.0 mA on a D3AA, which means the boost circuit has a higher power overhead than I thought. There’s no way the current drivers could operate at the power levels I was hoping for. To accomplish this “standby moon” feature, a whole new driver circuit would be needed. As far as I can tell, no currently-support hardware is capable of it.