No. TD status carries no work authorization at any point, so a partner holding it cannot take American employment, freelance, or continue working remotely for a Canadian employer from inside the country. A common-law partner is not a spouse for this purpose and cannot obtain TD status at all.
Two different problems hide inside the same question
The first is the scope of TD, which permits residence and study and nothing beyond them. A partner who intends to keep earning has to hold a status of her own that authorizes work, which for somebody in a listed profession may mean her own application rather than a dependent one. The second problem catches households that have never had cause to think about it.
TD reaches the spouse and unmarried children under twenty-one, and a long-standing common-law relationship recognized in Nova Scotia does not make a person a spouse for these purposes. A couple in that position either marries or plans two separate routes, and a preclearance counter is a poor place to discover the distinction. Children may enrol in school while in TD status, and a child stops qualifying on turning twenty-one, so a household with a teenager should map that birthday against the length of the assignment now.