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Due to a variety of factors (mostly the Royal Navy) the Germans would have lost even if they obtained air supremacy. The Germans did not have a very good airforce when it came to naval bombing (they would be forced to rely on Stukas), and concentrated naval power would be able to put up alot of AA. Nevertheless, a victory in the air war would have led to an invasion of Britain, even if that invasion would have failed.
As for the U.S. acting unreasonably, it is debatable (though I wouldn't say the British had and special naval rights!). Didn't Madison say though, that the U.S. would join the side that stopped 'impressing' their sailors? (the French were 'impressing' too, and actually got half as many as the British).
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