And what do you think the hydroelectric plant was doing with that power before the data center showed up? Dumping it in the ocean?
Of course not. It was going to homes and industries. Every watt of smug power that Google uses for their datacenters is a watt of hydrocarbon or nuclear generated power next door.
A datacenter with 10,000 servers may be more efficient because of scale than 10,000 homes with one server each. But if you are on grid power, each watt that you use comes from a combination of coal, nuclear and smug sources, in the ratio of your grid and the grids your grid is tied to.
Just because your local power utility company is willing to sell you the fiction that you are exclusively on one source or another doesn't make it so.