Although I'm not 100% sure, I am pretty certain the US mains system runs off spurs, rather than Ring's like the UK, so this is UK-centric.
If the plugs are on the same Ring Main, then you will likely be ok. Assuming no nasty spikes or noise on the line, you can expect around 10MB's throughput on an 85Mb/s device. Beware the cheap and cheerful specials, they usually sync at 14Mb's (With nothing about this lower speed on the box), and a <1Mb\s throughput.
Extensions, garages etc are fairly commonly run off different ring mains (Professionally done ones are anyway, what Joe Bloggs has done with some Twin and Earth, and a vague notion of red and black wires, I dread to think). If one Trip Switch runs all your sockets, you are probably fine.