It would be amazing if it could have a significant impact on spatial and temporal accuracy of things like rain.

That has to do with the forecast's grid size, along with some irreducibly complex and ill-conditioned physics that AI won't help with. The best general-forecast global models now have a 10km grid. Some specialist models go down to about 2km. So, depending on the size of your town, probably not fine-grained enough, though there are also point forecasts that take into account terrain, albedo and other fine-grained features and can be pretty accurate, especially when there are some good observation stations nearby so the forecast models can be continually trained based on actual data.