I would say, possibly yes, but depending on towns infrastructure.
Town should have some infractucture developed and available, for this to apply to it's citizens. For example, a tavern of certain level/quality, and/or some other structures built, that can be connected with food refinement, agriculture or something.
IF town is developed enough, and feautures all the prerequisites, then yes, my opinion is that such town could feature a "satiety freeze" function, for its registered citizens.
What about visitors you ask? Yes, but only for those visitors that have rented a room in the tavern / city motel. And not for everyone that simply physically enters the city. In this way city can have some revenue back from investing in those structures and features (structures that shouldn't come cheap and easy to be built).
TLDR: yes, if a city has all required infrastructure built, this could be available for it's citizens and for those visitors that have a room rented within a city.