Ans: No. Natural convection will not occur in zero gravity.
The density of the substance near the heated (or cooled) plate decreases (or increases) which causes the molecules near the plate to move upwards (or downwards) due to buoyancy forces.
The buoyancy forces will be absent in the absence of gravity.
So, in the absence of gravity, there will not be bulk fluid motion and the heat transfer between the plate and fluid molecules near the plate will be through conduction mode.