I live at one of the intermediate stations on the route - I'd be more than happy to change at Alty if fairs were reduced to get to alty. Currently - my station to Altrincham is the same price as my station to Piccadilly so it would cost me more to buy a Metrolink ticket for all zones. Putting this aside though, I agree with Chester1 above - changing for the Metrolink usually doesn't slow one's journey down.
My main concern is freight capacity on the route as a whole. A lot of freight uses the mid cheshire line and if it wasn't for the bottle neck at Nav Rd. I feel it would get a lot more use (IE moving all Hindlow/Tunstead to the south quarry flows to that route rather than half of them) - so what would be done about this if Alty to Stockport was to become part of the metrolink?
I wonder how much fares distort demand. Deansgate-Castlefield and St Peters Square are much better located for journeys for a swathe of the city centre compared with Piccadilly, which is served by Altrincham trams anyway.
Tram Trains and freight are compatible. Sheffield tram trains share some track with freight trains and South Wales Metro will too. Tram trains would limit capacity but a timetable could be designed, especially if the line becomes fully double track (with all Altrincham trams being tram trains).