Unlikely that a "full specialization" will be possible, given that the systems are webbed into each other. You'll probably not be able to focus entirely on a single yield, but instead need a bit of all of them, so it's likely that you'll need to specialize cities on different yields.
Then, when the basic requirements are met, depending on how strict the limitations for building more districts are, you'll probably have some wiggle room to specialize in whatever you want, and that may indeed come as an empire-wide specialization as in "When a city has the basics it needs I will always prefer build X if there's no obviously better thing to do".
At least that's what the system looks to me currently.