Do the Chinese have a (potentially politically incorrect) way of imitating English speakers? I do not mean to cause offence with this question; I ask only to potentially become better acquainted with Chinese vernacular, and, I must admit, a little out of curiosity.

A politically incorrect and borderline racist way for an English speaker to stereotype the sound of spoken Chinese is "ching chong ching chong" or variant thereof.

Do the Chinese have an equivalent standard gibberish for impersonating English speakers or other westerners?
Maybe it is difficult for English speakers to learn the four tones of Mandarin. 
When you read Chinese characters in a sentence all with a high level tone or falling tone, it sounds like a foreigner who has not mastered oral Mandarin. This phenomenon of imitating foreigners' accents always occurs in Chinese films and TV series.