Good guess but I don't think this is quite right. In gravity, the gasses that are rising are the ones that are hot; CO2 may have a lot of excess energy after the the combustion rxn so it is often hot. However some of those hot gases are going to be H2O vapor and also constituents of the air above the flame that didn't participate in the rxn but absorbed the heat. Since any gasses approaching the flame from the top or to a certain extent the side will get hot, the only gasses capable of feeding the flame come from below and to the side.

Now out of a strong gravitational field words like rise and fall start to lose their meaning. So instead of up from center of gravity and down to center of gravity let us divide the space(around the candle) into hampered and unimpeded. First off, yes we can see the efficiency of the burn is reduced without a density gradient due to a strong gravitational field. This doesn't mean that convection has completely failed. If this was the case the flame would have a far more turbulent shape to it. As it stands though the shape of the flame is nearly a uniform sphere.

The spherical part of the flame shows that the forces that drive convection currents are still at work. The gasses in the flame that are hot don't want to be near the other hot gasses and move away in a maximum dispersal pattern. The sphere is present in space relative to the candle that is unimpeded.

The flattened part of the flame is the only part of the flame close to solid matter. This is clear from observing the orientation and shape of the wick. In the absence of inflow any hot gasses escaping the flame would hit the candle and bounce off into other hot gasses, making that path less favorable. This ruins the uniformity of the sphere, creating holes. Now because the rxn is self sustaining and nature abhors a vacuum as the hot air rushes out cool air rushes in. The only break in the outflow is near in the hampered space of the candle and the inflow pushes the outflow away from the candle.