Yes in principle. A startup can qualify, but the funds must be irrevocably committed to the enterprise before the application, the amount must be substantial relative to the cost of establishing it, and the plan must show the business will employ more than the couple.
A startup qualifies once it stops being a plan
The treaty-investor category does not require an existing business; an enterprise that is about to operate is acceptable. What it requires is that the investor has already placed capital at risk. For a purchase, escrow tied to visa issuance solves that problem.
For a startup there is usually no counterparty to hold escrow, so the couple should expect to sign the lease, buy or contract for the roaster and espresso equipment, pay fit-out deposits and fund a working account before applying. That spending is genuinely at risk if the visa is refused, which is precisely why it counts. The amount should represent most of what this particular business costs to open, and the plan should show a path to hiring baristas and a production assistant within a few years.
The principal applicant must be a Canadian citizen, and Canadian nationals must own at least 50% of the enterprise; the other spouse need not be Canadian if those conditions are met. The spouse who will direct the business should be the principal applicant.