Your query has nothing to do with TK Miles & Smiles.

Essentially you would book and pay for the TK ticket, get your record locator, then call Aeroplan to upgrade. I'm guessing that there would need to be award space in Business Class (my last TK award was in "I") for Aeroplan to be able to upgrade.

Married segments may or may not be an issue, so you should check the full YUL-IST-CPH for I space.

Note that Turkish Airlines uses a different bucket for upgrades (J) which may or may not apply to Star Alliance upgrades since it's fairly generous (but expensive using TK miles).