I can confirm capturing a city with a Gunship my brother has done it as well. However I don't know that this isn't intended. I don't have access to the Civpedia ATM but in the manual I don't see anything that would indicate that gunships are not supposed to be able to capture cities.
Here is what the manual says.
Air Units
There are five main types of air units in Civilization V: helicopter gunships, missiles, fighters,bombers, and anti-air ground units. Helicopter gunships are the closest to standard groundcombat units and will be discussed separately.
Of the air units, missiles are essentially one-shot weapons: you fire em, they hit their targetand theyre gone. Fighters are primarily used to defend against enemy air power and toclear the target of interceptors to allow bombers to hit their targets. Bombers do damage totargets on the ground, if not intercepted. Anti-air units defend against fighters and bombers.
Helicopter Gunships
As stated above, helicopter gunships are quite similar to standard land units. They are extremely effective at killing tanks, but remain vulnerable to anti-aircraft fire.
Gunship Movement
Gunships can move over all terrain types including mountains and ice, at a cost of 1 MP
each. They can also move over coastal waters at the same price. They cannot enter deepwater unless they embark.
Anti-Tank Bonus
Gunships can do serious damage to tank units (which is why most armor is accompanied byhefty anti-air assets on the modern battlefield).
The capturing cities section also didn't seem to have anything to indicate they couldn't do that. Does the Civpedia entry say something to that effect or are we just assuming they aren't supposed to because they didn't in Civ IV
, but it's already known.
. But thanks for the update 
