I do believe they are. The challenge is not folding but the creation of the macromolecules from the chemicals which would have been on the early earth.
Water is very important. In particular, the combining of amino acids into proteins is thermodynamically unfavored in water. The key challenge is creating and bringing together the right macromolecules. At that point, nature (e.g. interactions with water) can assist in some of the assembly process.
The key point is that cell formation is very strongly disfavored near equilibrium, so most have moved toward non-equilibrium systems. However, those systems generate sources of entropy production which moves away from the state of life. NEQ processes also do not drive systems toward higher free energy and specified configurations of matter without the help of engines and information. Therefore, the chances far-from-equilibrium are no better than near equilibrium.
The key issue is not solely how life operates now, but how did simple chemicals coalesce into life.