On looking at a decent paper, instead of the freepress, it seem's that what the airport is after is a station on the current line, rather than diverting it. That would leave, depending on where the station is a short 2 mile bus journey.
They could sell this with a park and ride service into Doncaster also.
There are problems though.... For the Park and Ride there are no commuter services using that part of the route. They would have to have a dedicated train 'messing' with the fast East Coast traffic.
Also would the Operators agree to disrupt their fast travel times by stopping those services at a Doncaster 'Parkway'.
I don't think it's an easy sell...