Based on the differences described above (which not everyone will agree with, I know), I don't believe you can instinctively gap shoot, nor shoot instinctively using a gap approach. While "instinctive" sighting isn't really a true "instinct" (like gap shooting it's a learned process), that's where the sharing between them ends. One often hears that gap shooting 'becomes' instinctive, but since the basics of how the methods work are so fundamentally different, how can that be? Oil does not mix with water if tossed in the same barrel, even if they might at a glance appear to be one liquid. More likely, it's just that the shooter's level of familiarity with gapping becomes keener with practice, and so 'seems' instinctive. To 'mix' them in theory only serves to provide more fodder for confusion to those wishing to learn the intracacies of one method or the other.
IMO, despite some appearance of similarity, the two disciplines are fundamentally different strategies used to achieve the same result, each with their own pieces, advantages, and disadvantages. Anyhoo, that's my take on it.