Is cigarette smoke an example of turbulent flow?

The meaning of the Reynolds number is that the equations of viscous fluid flow allow similarity: if the geometry is matched (up to a scaling factor) between two setups, and the Reynolds numbers are matched, then the equations describing fluid motion are the same in normalized variables, which means that the character of motion (laminar or turbulent) should be matched as well. This follows from an algebraic transformation of the equations, and there is nothing there that would predict that motion has to become turbulent for $Re$ above a particular value, e.g., $Re$ = 1. On the other hand, the physical interpretation of $Re$ as the ratio of inertia to dissipation implies that increasing $Re$ should eventually lead to a transition to turbulence. However the numerical value of critical $Re$ depends on the geometry. In some standard cases, e.g., flow in round pipes, it is known that transition to turbulence happens at $Re$~1000; but this does not say that in a different setup a value as small as $Re$~10, in case of a cigarette, would not be enough to make the flow turbulent. So whether in a particular setup the Reynolds number is sufficient for transition to turbulence is up to an experiment (or a detailed simulation). For a cigarette, experimental results, e.g., in the picture, clearly demonstrate that initially laminar rise of hot air plume from a cigarette transitions to disordered, turbulent, motion of air a few cm away from the tip of the cigarette.

Below are a couple of insightful videos showing turbulent plumes from a candle https://www.youtube.com/watch?v=mLp_rSBzteI and from a match https://www.youtube.com/watch?v=TQJAokQQbmI