Yes, it is possible to redeem Turkish M&S miles for flights between two Canadian cities. You might be able to find availability online, but you will need to call M&S in order to book your award flight.
No airline has any real incentive to help you use miles on partners, who must then be compensated. They would rather you use the miles to fill an otherwise empty seat on their own plane, or let the miles expire.
When using miles, you must contact the program where the miles are banked, in your case, Turkish. According to the M&S redemption chart, a North America-to-North America flight, as a domestic flight would be, would cost 20,000 miles in economy round trip.
The Turkish Airlines website, however, does not let you search for award seats across all its partners. In fact, this feature is rare among airline websites in general. The fares that award tickets book into also tend to be hidden from search engines like the ITA Matrix. Your options are as follows:
- Search on ANA or Air Canada, call Turkish Airlines to book
For Star Alliance, for the last decade or so, there have only been two decent options for search from airline websites: Air Canada and ANA. You would need to create an account with Aeroplan or Mileage Club respectively, log in to their website as if attempting to redeem miles in those programs, then find the right options to search for Star Alliance award availability.
ThePointsGuy.com has a detailed blog post on searching Star Alliance award availability, including screenshots, that walks you through the process as of November 2015.
Note that the award levels and restrictions will not be accurate. Even among alliance partners, mileage accrual and recemption levels and rules are rarely if ever reciprocal. In other words, a flight that costs 20,000 M&S miles might be 15,000 or 30,000 ANA or Air Canada miles.
Also, as airlines may allot award seats for their program "natives" before partner participants, Aeroplan may show seats that you cannot book with Turkish miles.
- Search on ExpertFlyer, call Turkish Airlines to book
ExpertFlyer is a paid subscription service that provides access to seat and fare availability on most of the major international airlines. I have not used it myself in many years and cannot speak to its current accuracy or cost, and do not know if there are other, competing services now available. I do know that the ThePointsGuy, again, has a guide to searching Star Alliance awards with ExpertFlyer.
- Call Turkish Airlines to search and book
Regardless of how you find the seat, you will still need to call Turkish Airlines to actually redeem your miles. Neither Air Canada nor any other partner has access to the M&S member accounts. So you could simply try calling the airline and have them search flights for you the old-fashioned way.
Finally, note that you may be subject to telephone booking fees. You will also need to pay for any taxes and fees associated with the flight, including fuel surcharges (YQ). Historically, I believe Air Canada has not charged YQ on partner redemptions, so you at least you have that.