No it was based loosely on Washington Depot, CT. I don't ever recall them mentioning Waterbury. In the original they say the town is near Woodbury. They also say SH is near Woodbridge at other times. That might have been an oversight confusing those towns over the years since they sound similar. Washington Depot is an hour from New Haven and an hour from Hartford. They got that right.
It always bothers me how off their portayl of Hartford was. Richard Emily live in the West End, the small Rich section. They negated the fact that Hartford is actually quite dangerous and a lot of people who live there are far from wealthy. They acted like it was entirely ritzy and full of privilege like Northwest CT towns. They ignored the crime rate. One time Rory goes alone to catch a bus later in the day and Lorelai acts like that's okay. But they portrayed New Haven more accurately, especially with Paris and Doyle's apartment.
my friend lives in Southington. and parts of the SH set, especially on the Netflix 'fall' episode when Rory goes into the gazette just reminded me of Southington.