There is almost certainly an impact somewhere, but I don’t have the data to know where it is. My conjecture is that a localized mass of steam would cause convection currents and drive microweather phenomena, especially downwind of such an air cooled facility. I’m not sure rain is necessarily the result, unless there’s a sizable mountain downwind, since although hot air will rise, it might run out of steam (pun intended) before cooling down enough to fully condense out. So it might just be adding a layer of humidity that floats a few hundred meters above the surface.

But even that could be devastating, if said layer blocks natural convection currents over a downwind town or city. It could act as a thermal cap, making that town warmer at night, because heat rising from the city would meet that humid layer and get absorbed by the water. The thermal capacity of water comes into play again, but this time against the city.

Heat energy is a driver for cyclones, such as when the warm, moist water of the Caribbean accelerates air as it approaches the southern USA, and only once landborne does it start to slow down due to drag and losing its energy source. I doubt we’ll ever have an AI-induced hurricane, but in a situation where there’s already an energetic weather event, it cannot possibly help to be adding heat to that situation.

I defer to the meteorologists to say what happens to the local weather and climate, and biologists on what happens to humans and wildlife. But I can’t see it being good, no.