Non-capitalist enterprises do not exist because all enterprises, along with their participants, are rewarded by money or other forms of capital. A free market does not exist because freedom today is at best an absolutism defined and controlled by a stale oligarchy, not by you. Quite the opposite of free indeed.
Hence your question, stemming from a plethora of definitions in economics left poorly normalized, up to wild interpretation and ambivalent no matter the outcome, reduces down to: “Does a marketplace with no remuneration create a pretense of freedom?”
From my intro, I think you can answer that question for yourself now. Get your mind out of the gutter of any derivative of classical economics, if you are curious to a better future.
