I can see three or four situations where this would be really useful:
a) If the foot tunnels under the Thames are shut at the same time again.
b) For getting bikes between the two Stratford stations rather than wheeling around the shopping centre.
c) For getting out of Canary wharf. The first time I biked through there, it seemed like every diversion around building work/one way roads with no footpath beside then took you back to the station (probably wouldn't happen today with GPS of course).
d) When you break a chain, or blow your last spare tube and need to get somewhere, it'd be a very nice get out of jail free card.
Apart from those situations though I can't see it being terribly useful because the stations are pretty close together and needing to go up or down to get to them that unless your destination was literally right next to the station, you'd be better off biking directly to where you wanted to go.