Yes, that duct is the feed into the HEVAC system from the blower fan (the housing of which is just on the LH side of your last pic).
That duct connects to the AC evaporator, as all the air fed into the HEVAC system goes through the AC system first, and then into the heater box where it's blended warm/cold, and directed to the correct vents.
So in short, yes, it is possible for AC water to get into the bottom end of that duct.