Is it acceptable to use the phrase "potted history" in a US text
The oldest use of the term "potted history" that I see off hand is in the American magazine The Galaxy, September 1873, in an article by American George Edward Pond writing under the fake name Phillip Quilibet:
If I skip the lad's measures and tidbits of potted history...
So it isn't necessarily a British phrase.
Recently there was an article A potted history Nature 525, S10–S11 (24 September 2015), about pot!
My guess would be about 0.5% of Americans would know what "potted history" means. I definitely never heard of it.