The issue with longbows isn't the effectiveness of the weapon, but the amount of training necessary. It takes years to train a good longbowman, which is decidedly not the case for crossbows or muskets. Unless you already have a culture of longbow use in enough of the population the effectiveness of the weapon is moot.
Which is why it's -so- good during many of the medieval wars before the primacy of firearms.
People used Bows of various kinds to hunt, to fish, to compete in fairs and tournaments, and to show off! So having an army's ranged units centered around archer was super effective. And if that had been the state of America during the War? WHOO DOGGY would it have been -hyper- effective at ending the war with a quickness!
But. For the better part of two centuries, the musket and pistol had usurped the place of the bow in the hands of the common man. Just an afternoon of training was enough to send your eldest son into the forest to come back with a few rabbits or a deer, after all. So much easier than learning how to use a bow!
Had the continental army tried to use archery they'd have been at some disadvantage. Enough of one to lose the war?
shrugs No one alive can say. Maybe the army would've gotten "Enough" accuracy pretty quickly to be useful in killing the redcoats as they stood in their nice neat rows and the archers hid behind trees, rocks, and other objects while spread apart to limit the utility of volley fire. The fire rate certainly would have been nice.
But then there's the -cost-. Making lead balls and gunpowder had gotten fairly "Easy" by this point. But actually making arrows remained (and still remains) a time consuming process. Not just for the arrowheads, but for the shaft and fletching themselves, which took a goodly bit of expertise and delicacy to manage.
While fielding -some- soldiers with Longbows might have increased the efficacy of the Revolutionary Army simply through continuous fire, the amount of effort involved in maintaining such a military diversification would've been fairly high.
Because fielding archers was hard. Especially when you did not use them regularily. The bows and all the arrows needed to be hand crafted and the training to use a bow (not accuracy, but strength) took years. Good when you had those people, but when not you can't simply raise some archers when you need them.
Very -VERY- True. Every word.
Though... in retrospect. Recurve Bows and Composite Bows would have been a different direction to go. Get within 30ish yards of the Red Coats while they're reloading and start loosing arrows from a Recurve Bow with a 25-35 pound draw weight?
Could've been useful, at least. Still expensive for the arrows if nothing else!