Assuming you don't have to mix in the priming sugar if in a conical?

[BVilleggiante]

I'm carbonating in a pressurizable conical for the first time. I just poured in the priming sugar today. Assuming I don't have to mix it since it's one single vessel?

 

[DSorenson]

Though I am not familiar with this process, I would assume that mixing it not mixing should provide similar results, since it will all convert to CO2 in the same system. Not to mention that, provided enough time, it should mix itself.