Hello Jake
I think more likely that cannon represents the "chaser" gun. The idea being to have a long gun on the spar deck that can be moved across the deck as appropriate to lob shots at a fleeing opponent (or hapless merchantman) in hopes that a well aimed shot (or a lucky one) will take out a critical spar and slow her down enough to be overtaken. As you point out, Old Ironsides was armed primarily with carronades on the spar deck (at least during her "glory" days)... Wonderful guns in terms of light weight, small gun crews, and ferocious smashing power, but with the distinct disadvantage of short range and limited accuracy. This makes access to a long gun imperative. I would think, however, that the 24 pdr represented in the kit was not appropriate... A long 12pdr or even 9pdr was more likely. They needed something nimble and able to fire rapidly.
If you'd like to add a nice detail... Constitution's carronades were a hodgepodge of types accumulated over the years. In fact, commodore Preble bought some from the British during his Barbary campaign. You could show some with screw elevation (and slightly modified carriages) in addition to the quoins shown on the model. You'll see this on the restored ship if you find the right photos.
How adventurous is your client? I've always advocated using the Corne paintings commissioned by Captain Hull as a basis for the paint scheme. The ends are trimmed in white, but the stripes and lower masts are yellow ochre. The Gallery windows are trimmed in red. Very striking and different from the usual ho-hum white stripe... (I think Captain Hull hurriedly painted over the white stripe after he was chased into Boston by Broke's squadron at the outset of the war to make her look more British before heading back out for his appointment with destiny vs HMS Guerriere).
After I complete my Heller Victory, and my Trumpeter Arizona, I'll take another crack at the 1/96 and put my money where my mouth is...!