Great General question

If I were to use a GG to citadel bomb next to a rival city, would that city become mine?
I have not tried it yet, but am tempted just to aggravate Alexander....

No, but each of the six hexes adjacent to your GG (excepting the city center itself, if you are that close); will become your territory.

When at war, your citadel next to a city will damage garrisoned units (including air), but does not damage the city itself.

Be forewarned that when cities change owners, they automatically get the six hexes next to city. So if you conqueror the city but the AI captures it back, you lose the couple hex you stole and the citadel.