I live in Georgia and want to go to Connecticut for a few months can I still ...

You would have to submit a formal request to Uber of your location changes. If you just open up the app in Connecticut, you won't receive any requests. 

They are usually pretty good about allowing you to switch.  However, the state laws and local Uber may come into play.  For example, if CT states you have to have CT license plate for you to function a rideshare, they obviously won't approve your request. You'd have to formally change addresses, update your registration, and get a CT plate first. Yuck, I know.

Uber currently doesn't allow temporary city changes though I am not sure why you couldn't request a permanent city change twice so that you can still earn income over those months you are in CT.

Keep in mind that you may have to get your car inspected each time you change locations which will eat into your earnings. Depending on the state you also may have to register your car in the new state which wouldn't be worth it, IMO, for a couple months.

Here is some more information on switching cities.