As you guys already know, the experts definitely don't agree...on much regarding archery. I shot 28 years RH. About 8 of those without sights (I won't say I was instinctive because I don't believe I ignored the arrow point or the "gap"). I've shot LH (to match my dominant eye) for 15 years. I shoot sighted compounds 20% better (scores on 3-D) LH with both eyes open. I've not been back to recurves very long -- began dabbling in 2001 getting serious the past two months -- challenge of it. I don't yet shoot the recurve as well LH as I did as a RH with left-eye shut. However, I practiced a lot more when I was in my teens and early twenties (recurve days). In archery, both hands do something very important, which hand holds the string or the bow isn't as important as bringing the string to the dominant eye side of the face: better depth perception, peripheral vision, and for some folks better balance. Frankly, I think wrong-eye shooting and subsequent closing of the dominant eye promotes target panic because too much focus is placed on aiming instead of active bow arm and drawing arm/back for proper follow through. I can tell you of one person who shot 32 years (North Dakota) RH. Two days after switching to LH to match the dominant eye (sans sights) he was thrilled to be shooting better than he had his entire life (his claim, not mine). Must one match string hand and domiant eye. Of course not. But you'll have to take that dominant eye out of the picture a bit by closing, squinting, or "fuzzing" it up a bit to make the right eye be "dominant". I would strongly encourage (but never insist) that a new archer definitely match up with the dominant eye. I've seen the positive results many, many times.
Having "said" all that, a pure instinttive shot (if there is such a thing -- and I'm sure there is but much more rare than most believe)probably doesn't need to consider eye domiance. They will shoot enough to "learn" to feel proper windage and elevation ... or miss trying.