Earls court station sucks, and you wait forever for a district line train going towards wimbledon. The only type of departure board is a printed list of destinations, with an arrow back-lit by a globe when your train is next. It has you switching platforms willy-nilly, and gives no indication of how long a train will be. If wifi could give extra information, fantastic.
The wifi probably won't get much out to the outer portions of the underground network, but I know the western picadilly line has non-functioning signage, due to there being no data connection from those stations which would allow them to have estmated time of arrival of net train. The electronic signs which would allow this just display "picadilly line" instead of any useful information. I had to use an application on my phone to get this information even while standing on the platform.