Could the USA of won the Revolutionary War with the 22 LR rimfire?
What you forget is that at that time, Britain had some kind of manufacturing establishment, whereas we didn't. This means that if we had the .22's, they would have had them as well, only more of them.
For the most part the Revolutionary army was equipped with a hodge podge of already outdated firearms, bought on Europe's surplus markets with the political and financial support of France.
Now, that would be an interesting question. Could the USA have won the Revolutionary War without the political, financial, and military support (they kept the Brits engaged elsewhere) from France? Probably yes, but it would have taken longer.
Now, to be sure, they did not help because they liked us, but because they disliked England.