It's rediculous what they come up with sometimes. Unless there are written set ordinances (which are sometimes confusing and contradicting) that you can Google or find through city for your city, and you don't have objecting neighbors...I don't see why it would be a problem. Chickens are becoming more and more popular as pets and also have economical worth for many families now. People like to know where their food comes from, and with a flock of chickens they can utilize everything, eggs, chickens and whatever else!
I live way smack in the city too. Major crossroads and butt to butt houses. At any one time I have 15 chickens (seems like everytime I get rid of one I get one or two more for some reason) and I have had crowing items on the yard for almost four years now and no one has said otherwise. My city is ready to throw out chicken regulations because of the high number of fowl fanciers who fought the city-including me writing to all the council-peoples fighting cause against them. I have 7 roosters and always high producing and male lined chickens that give me all roosters usually. They start crowing, no one cares. I convinced our new neighbors to get chickens. They love animals and he got himself a nice trio of show looking game bantams and I recently asked him if he wanted three roosters I had for free to do whatever he wants and he took them. We have a very small yard mind you.
My point of my long blah blah I guess is, if your city doesn't have rules (and they just want to play bigshots) I see no reason you can't keep your chickens as long as you keep up on the cleaning, there are no foul odors, you keep the chickens cooped or free-ranged but under somewhat control by wing clipping and such and providing that roosters don't cause any nuisance. Ask your neighbors how they feel about chickens and offer them eggs and chicky poo for lawns and garden. They may feel differently later
When he calls back, ask him everything you can think of for any questions you may have and ask that he send you all the city ordinances, rules and regulations and what any requirements may be.
Also, I see no reason to take down your coop either for not being a permanent structure unless it's a huge eyesore for the neighborhood....