No it won’t. Uber and Lyft will operate identical to how it is today. They will outsource the HR and employment issues to staffing agencies.
Drivers will simply have to be “employed” by one of these agencies and then go about driving the same way they are now. These agencies will likely allow their “employees” to drive for whatever companies the agencies have agreements with during their shift and call everything over minimum wage “incentive pay”.
Uber, Lyft etc will contract these staffing agencies and pay them per ride instead of the drivers and the agencies will passthru that income minus their cut.