Absolutely, it would be possible. However, extremely unpractical.
The
current keel-cooled
refrigeration systems, such as Frigoboat, use a
keel cooler that is about 5" x 10" (going from memory) to serve a Danfoss BD 35 or 50
compressor. These compressors are capable of, say 300 -600 btuh, depending on several variables, using this
keel cooler.
A 12,000 btuh AC unit would then theoretically require a keel cooler of approximately 20-40 times larger (likely even more since efficiency decreases when scaling up). Perhaps something along the lines of 20" x 50" up to 36" x 58" or more. This would be a sizeable device hanging from your
hull.
Due to the different duty cycle of an AC unit as opposed to
refrigeration duty, the keel cooler would have to be increased even further as the ability to condense the hot gas refrigerant would deteriorate as the keel cooler warmed up, as well as the adjacent water warming due to the heat of rejection.
On the other hand, some large slow-moving
motor vessels do utilize a keel cooler for
engine operation. These are a different application, though appear to be beneficial for boats such as large trawlers for
engine cooling.
Interesting idea though.