On your week off you don't have to be there. You could take advantage of the cargo system or Airnet jumpseat agreements and commute. When you are on call for those 2 other weeks however you do need to be at your base. Also, if your base/plane is short staffed you might be on call longer, they pay you more for it, but then you would be there all the time. If you have any kind of family you would want to live where you are based with Jetride. Even if your single your going to need a semi-permanent place to live. I don't think a crash pad would cut it. There have been weeks where we didn't fly at all. I know I would want at least a studio apt or something.
So are your required to live there no, not even as a PIC, you could certainly do something short term in hopes of a different plane opening up in a different city.