It will interact to the extent that temporary foreign workers and students in Canada are already a major source of immigration to Canada. People apply, not just from the live-in caregiver program, but from other temporary foreign worker streams to be skilled tradespeople, skilled workers, especially to enter Canada under the provincial nominee program.
So yes, there is a very direct connection, but these are different programs. The temporary foreign worker program is not in itself an immigration program, but it can bring people to Canada who then choose to apply to immigrate.