Almost. I am talking free market, and supply demand pressures. Supply and demmand pressures are not free without private ownership (at all levels). The moment you exclude any group from any form of private ownership you no longer have a free market and no longer have free supply-demand pressures.
Supply and demand exclusive to a privilaged group (worker cooperatives in this case) is not a free market with free supply demand pressures, it is a market that has, at least partly, fixed aspects of the market.