Could a Canadian nuclear-submarine programme have led to AUKUS membership?

If Canada had acquired the Canada-class submarines, could it have become part of AUKUS?

Canadian participation is considered plausible in that alternate history, given the countries' existing alliance relationships.

The premise gives Canada an established nuclear-submarine programme through the proposed Canada class. Participation in AUKUS is considered plausible under that condition. The reasoning rests on the existing network of alliances connecting Canada with Britain, America and Australia. No detailed arrangement for Canadian participation is proposed.