That's an interesting connection that, to be honest, I don't think played a great role in being opposed to further European colonisation and|or influence in the New World.
I see it more as the beginnings of US regional Hegemony and notable for two things, how it began and future attitudes to world affairs.
In the beginning (from the wikipedia link):
Great Britain shared the general objective of the Monroe Doctrine, and even wanted to declare a joint statement to keep other European powers from further colonizing the New World. The British feared their trade with the New World would be harmed if the other European powers further colonized it. In fact, for many years after the doctrine took effect, Britain, through the Royal Navy, was the sole nation enforcing it, the U.S. lacking sufficient naval capability.
This is a
reality of just how intertwined the actual USofA and the actual Great Britain were, despite that whole little hiccup with "Independence".
In real politik the thirteen colonies were business investment startups by British Venture Capitalists who retained contacts, contracts, and business ties after reducing the meddling abilities of that pesky king in finnancial arrangements.
The now independent colonies and new independent nation remaind largely Anglophile while the old order saw no conflict of interest in the use of their navy in the defence of mutual interest.