
Daniel W. answered 06/17/19
Kind and Knowledgeable English, Latin, and Theatre Tutor
"had the Chinese not come under foreign influence" is a conditional clause, synonymous with "If the Chinese had not come under foreign influence." The first half of the sentence describes the result of the condition. You could rewrite the sentence to read, "If the Chinese had not come under foreign influence, the significance on Chinese pottery may have remained clear."
An example of a similar conditional sentence would be, "If I had stayed out late yesterday, I may have overslept this morning" (or, alternatively, "I may have overslept this morning had I stayed out late yesterday").