It depends. If it's so flat that it can't power the computers and pull in the contactors, you are like an ICE owner that needs a jump start.
But as long as it has enough for that, as soon as the contactors are pulled in, the DC-DC will start charging the 12 V auxiliary battery.
Note however that this will only gently charge it, at about 13.5 V, not at the 14 V or more when the car is in ready mode. I think that the reason for that is that a charge might be 10 hours or more, so that there is actually a chance of over-charging the battery, whereas when driving, it's often much less time. I think when driving, a computer also monitors the auxiliary battery charge current, and if it falls below a certain level for a certain time, it deems the battery full and drops back to the ~13.5 V float voltage. The auxiliary battery can be charged indefinitely at the float voltage without risk of damage from over-charging.
So if you find yourself with a flat or nearly flat auxiliary battery, and you are at home where you might have a 12 V battery charger, it's a good idea to charge the auxiliary battery while the main battery is charging. That way, the auxiliary battery gets away from the dangerously low state of charge the quickest, and therefore has the best chance of recovering fully.