We do not have free-markets today because we have yet to set freedom free. We do not have sustainability today because sustainability can only exist as a function of strict principles of renewability. Which boils your question down to do two things that do not exist today tend to exclude each other? The answer, of course, being, no.
If we assume your stated presumptions to be factually accurate and implemented as desired, the answer is also no. For a free-market must be subjugated to a relativity theory of freedom to yield a dynamic meritocracy that continually renews the marketplace in question. And from the latter renewability will come a prolonging of sustainability. So, marketplaces that adhere to the proper principles of freedom do indeed prolong sustainability.
The problem is we have no modern principles of the relativity of freedom instilled in the marketplaces we built. The reason why I am reinventing a new operating-system for humanity, one that unleashes the freedoms needed to prolong the sustainability of humanity.