An odd argument and an odd destination pair to choose.The other thing to note, is that rarely are people traveling from airport to airport. Now given that rail allows travel from much closer to home to much closer to where they are going to it is likely that the associated travel emissions for rail are lower.
Take for example someone living in Winchester and going to Manchester, if they go by train they can join at Winchester Station and travel to the city centre in Manchester. If they are flying they would have to travel to Southampton or one of the London airports (which could even be Luton or Stansted) and then from Manchester Airport to the city centre, which could add a fair amount of carbon emissions depending on how they travel. It's not unlikely that such emissions (potentially not in this case, but generally so) could be car based, so the switch from flying to train would likely reduce car emissions as well as aviation emissions.
The options for your suggested trip are
Car - About four hours. Fuel cost about £70.
Train - Again about four hours plus time to get from and to the station at each end. Train tickets £297 peak £127 off peak
Plane - 1hr 10 min flying time plus travel to airport only two flights a day on a 72 seat ATR. Ticket £211
So I would suggest 9/10 people, and freight for that matter, drive. Your suggestion that someone would travel from Winchester to Luton or Stansted to get a plane to Manchester is not realistic it a completely doglegged journey.
On an emissions basis I would suggest an ICE car wins then the ATR 72 and last the mainly Voyager rail journey.
As regards transport to the airport if its city centre most would use a train and in most cases these would be electric other local destinations I would guess car or taxi possibly bus. But the effect on emissions of the short connecting legs is again minimal.
The relevance of HS2 I suppose it could attract custom on the Winchester - Manchester route but it would involve either a cross London change from Waterloo to Euston or one at Reading so not as convenient as XC so a marginal benefit. Meanwhile more of the ICE are becoming electric.
Out of interest what car do you currently drive?