No, no-living matter does not have consciousness since consciousness requires a "receptacle" in which the "thing" can be conscious, which is possible only if it has the capacity of manipulating ideas, thoughts, imaginaries, ... i.e. if it has a brain.
In other words, only living matter is susceptible of consciousness, but not all living things have a consciousness in the sense that we employ. Rudimentary life forms such as worms, bacteria, virus, do have a primitive form of consciousness even though they can hardly be said to be "conscious".
For Stéphane Lupasco, consciousness results from the antagonistic relativization between biological matter and physical matter. He argues that this relativization engenders a matter of a Third kind and he calls it psychic matter or quantic matter.
Stéphane Lupasco, "Le Principe d'Antagonisme et la Logique de l'Energie", mann & Co., Paris, 1951.