Nope. That would be putting all the load on one or two teeth, and it would fail. The cog belt runs on sprockets that have many teeth engaged at all times.
That is a useful observation, perhpas qualified with "depends on ratio and diameters involved"?
IOW system where the pinion is a substantial part of the volume of the drum (have not checked to see where things begin to interfere) but say 3:4 or 7:10. Drum size "largish" - needs to be somewhere over 8" or 9" given the belt diameters available for, say 75 HP. At that point, then, the issue becomes derating (overbuilding) & whether the weight advantage continues to apply?
I'm wondering about thermodynamic issues.
Presumably the drum could be alloy, finned &/or ventilated at some energy cost.