Not necessarily. An organic molecule doesn't just have to be made of carbon. There are many molecules consisting of carbon that aren't organic. The classification however is highly arbitrary. CO2, graphite just two off my head that are carbon containing non-organic. Carbon in rocks would be mostly inorganic.
A comet has hydrogen, carbon, nitrogen, helium, and many more simple atoms. Space is full of things such as radiation, heat, cold, gases, pressure and other chemicals that facilitate the formation of simple compounds via natural chemical reactions. Chemistry can happen anywhere. That's really all there is to it. Creating organic molecules is not hard...getting organic molecules to form more complex structures leading to life is the hard part.
To clarify, gases like methane, and simple alcohols are small and organic. Both of these (and many more) have been identified in space already.









...all organic compounds have carbon....all carbon compounds are not organic.