I'd argue the effect may be the opposite. Tenant protections lead to homelessness by forcing landlords to be selective against vulnerable peoples, making it harder to get back on their feet after difficult times. Risk in renting to these people is greatly reduced if you can toss them out as soon as they stop paying.
Either way, you’re making someone homeless, which is an intractable problem as long as the housing demand exceeds supply. The only change being made is the criteria for who gets to suffer.