That's a
big IF.
A big part of how air conditioners cool the air is by removing moisture/humidity from the house/room, which is usually closed off from the outside environment.
Most swamp coolers
add humidity to the air from the ice melting,
often leaving the air feeling even
more oppressive.
This is the best DIY swamp cooler design I've seen, tho I haven't searched extensively.
Depending on how water tight that ducting is, it should not add any humidity to the air from the melting ice.
Wonders if plastic flexi-duct would be a better choice because it's water tight?
Condensed water from the air moving thru would collect in the ducting, how to drain that?