Sure, but pretty much every Uber driver I've encountered also drives for Lyft and there doesn't appear to be any mechanism by which Uber can prevent that.
Uber is actively developing ride experiences like UberPool and UberHop that link multiple riders together in ways that can avoid a driver's car ever being empty. If the car isn't empty, they can't turn on Lyft.
Lyft Line does the same. As far as cars not being empty, during non-peak hours the streets of San Francisco are filled with Uber cars driving around with no passengers. I guess Uber Eats or whatever is supposed to fix this. No passenger? Stick a salad in the passenger seat.