Wireless communication is widespread enough that I don't think it matters too much where Watson "lives". The inputs and outputs required from "him" (for questioning, anyway, not for training) are tiny, so bandwidth isn't much of a concern. Assuming the architecture for it is parallel enough that it can be responding to lots of people at once how much it is distributed vs hosted on one system isn't particularly relevant to its usefulness, IMO.
I question how well Watson would handle single questions at a time being asked compared to the millions of requests a day it would get if it was setup like say, Siri. Not that you are wrong in any way, they could certainly scale into an even bigger server farm and use the internet to deliver the questions and answers, I just wonder how much more server's they'd need.