Are same-sex partners classed as common-law if living together?

Yes.  Under Ontario law, unmarried lesbian, gay, or same-sex partners are treated the same as opposite-sex couples; as long as the partners meet the established legal test for common-law spouses, there is no distinction drawn.

For example, to be eligible to claim spousal support from each other, the provincial Family Law Act requires only that they are “two persons” who have been continuously living together in a conjugal relationship for three years, or if they have a child together (by birth or adoption) then they must have cohabited in a “relationship of some permanence.”

For these purposes, it does not matter what gender those “two persons” are.