Sebas: they do that, yes. Go the whole hog... use your starting treasury to pump out HA. queue them up so you get a steady supply for the next 10 turns, then besiege all the nearby cities with 2 HA units and let them sally out at you. Then shoot them to pieces :) With 2-3 HA a city you should be able to take 3-4 in one breath once your building is completed. Then, just wait (or keep conquering) until your treasury goes back into the black. Exterminate some.