Well, no. The AI data centers have to buy their electricity just like anyone else. Maybe they get a better price per kwh, because they buy so much.
However, increasing electricity costs will encourage the power companies to build more power plants. The biggest problem here is government intervention and over-regulation: for the kind of power these data centers need, you really want modular nuclear reactors. Dozens or hundreds of reactors of the same design, because that's what would make them economical. Sadly, that's just not possible in the current regulatory environment.
To be clear: I have nothing against the data centers, or the energy requirements. Energy is civilization, and every major civilizational step has been enabled by a step-increase in available power: muscle power, horses and oxen, water wheels, steam, oil, and most recently nuclear. Renewables are not even relevant: they may replace fossil fuels, but come nowhere near the power density of nuclear.