For example, centralised servers have far more chance of being run by renewables than your home computer. Google for example, is tending to do stuff like build their servers near hydroelectric plants or where there's wind farms or solar available.
So outsourcing your needs CAN actually be a good thing; and if everyone did it, it's a net positive.
No, it's a net negative Building your server farm near hydroelectric plants doesn't reduce the amount of fossil fuels burned. It increases them. The entire electrical grid is connected. If Google's server farm weren't there, the hydroelectric power would be transmitted to fill a need somewhere else. All Google does by locating their servers there is cause someone else to use fossil fuel power instead of hydroelectric power.
Put another way, certain power plants produce as much power as they can (wind, solar, to some extent hydro and nuclear). Other plants scale their production so that total generation matches demand - coal for day/night variability in demand (they're shut down overnight), gas for instantaneous variability in demand. If you add a server farm on the demand side, it doesn't matter which power plants are nearest to it. The net effect is that additional gas and coal must be burned to handle the added power demand.
The only way to add a server farm and reduce fossil fuel consumption is to build additional non-fossil electrical generation capacity along with it.