I know it goes to Victoria as it is, but it wouldn't require a tremendous amount of engineering to connect Picadilly too.The solution to many of the transport constraints is in the bottom LH corner of that photo
If they reconnected the fork from just before Ardwick station to the Enterprise on Ashton Old Road, you could have a direct route from Picadilly that I guess would take about 3 mins in each direction.
Although it would give Manchester a loop between Pic and Vic, it would involve (re)building two small bridges, so its not going to be cost effective for 20-30 events (matches and concerts) a year, but maybe if there was an arena....
Even running a train as far as Ashburys, then running it in the other direction and going up the other fork at Gorton Road would be a solution.
I suspect Northern wouldn't have the spare capacity though anyway.