The subways will stretch out to all major Centres surrounding Toronto just as it is already started, and currently being designed and built. It is really nothing comparable to GO which acts mainly as a funnel from non-central Southern Ontario locations into Union station.
This GTA subway backbone is well underway with North York, Vaughan, Scarborough, soon to be Richmond Hill. Mississauga (Etobicoke West) has been lobbying (simple google search) and waiting to get in the que. The Sheppard subway will be built and will be set up the link for Pickering there just as LIne 2 will already have set up the link for Markham in the future.
That's an interesting concept, but I believe we should look at each connection separately; not all of them are equally viable.
1. Yonge subway to Richmond Hill: certainly justified, lots of potential ridership, just need to add the Relief Line in the south.
2. Vaughan subway: already there, but wasn't a very good idea, the ridership north of Steeles is extremely low. Vaughan Centre is not really an established urban centre, just a potential one. The subway could terminate at the Pioneer Village instead.
3. Mississauga: my best hope was to use the Milton GO line for a direct connection between the Toronto and Mississauga downtowns, but it looks like the CP mainline is untouchable and the Milton line idea is not going anywhere.
Maybe, the best bet at this time is a branch of Line 5 (Eglinton) running into Mississauga. A Line 2 western extension may be considered, too.
4. Markham: I would not extend the eastern end of Line 2 further north from the Sheppard & McCowan terminus, due to the travel time concerns and operational stability concerns. Plus, most of density in Markham seems to be located west of McCowan.
Instead, I would eventually send the OL / Don Mills line into Markham. Either up Woodbine, or diagonally to the Enterprise area and Downtown Markham.
5. Sheppard Line to Pickering: there is an appeal in connecting the Sheppard corridor to the Lakeshore East GO line, that would enable many new transit trips and maybe even compete with driving on the 401.
However, both the route and the technology would have to be scrutinized. It should be something fairly fast, running at much higher speed than most of TTC's subways, and at the same time, it does not need the 30K+ capacity.