In the land of infinite operating dollars, they would interline and both run Downsview Park to Vaughan.
More realistically, the Sheppard line just needs to run to Finch West, to connect to the LRT. They built a wonderful crossover structure at Finch West, so it's a good turn-back point. People can change trains to go to York U.
Interlining makes sense for areas where you have lots of traffic. Interline through downtown, and branch in different directions in the burbs. Interlining through the lowest-use section of Line 1 makes no sense, nor would I think there'd be the capacity on Line 1 to support it, where they are already planning to fully utilize the capacity south of Finch West.
Running to the transfer point at the Downsview Park GO station might make sense - but you'd still need to run a double set of tracks, as you can't be running a Line 1 train every 2 minutes, and then add in a Line 4 train every 6 minutes (or less, given the likely lack of demand west of Yonge).
I'd think a better solution in an infinite world would be to keep running west from Allen/Sheppard (Sheppard West station aka Downsview Station) under the airport to an additional station at Sheppard/Jane and then north on Jane to Jane/Finch to intersect the LRT. Why run 2 lines together, instead of running them in different places.
My main point is that I think this is a more useful connection to the city than the oft-cited interline to send Sheppard trains south to downtown, which as far as I can tell, is only really useful as a North York Centre<->Yorkville shuttle.
And the main question it leads to, is what would be the ridership. I have a hard time thinking that it would even be the existing 5,000 an hour on the Sheppard subway, west to Yonge in AM peak.
There's no need for BRT on Sheppard West. The 84 Sheppard West is already very speedy. I've taken it several times when crossing to Yonge Line from Spadina Line
Indeed it is! But it's not a particularly busy route. But the 196B only runs 10 times an hour in AM peak (compare to the over 30 times an hour on the 196A branch from Downsview to York). That's only 530 riders per hour. Even if you add in the 86 Sheppard West, it only has 14 buses an hour - 750 riders per hour.
Ideally, you'd be looking at 15,000 or so to consider subway. Surely, you'd need at least 5,000. At 750 riders an hour you don't need much more than one 4-car subway train an hour. Assume that demand triples because of the convenience of subway - you can run one every 20 minutes. Sure, I'd expect it to go up somwhat ... but I'm not seeing the demand. And honestly, I'd expect most of it would be getting on at Bathurst.
As Pasternak pushed the TTC to actually study the feasibility of the "North York" relief line, perhaps we'll see some estimated numbers for subway ridership - which should be similar if the service terminated at Downsview or ran through to Vaughan.