I, as a native speaker of English, am quite familiar with the pronunciation quirks of people of many different nationalities when they speak English. I have heard in passing people from probably half or more of the countries in the world speaking English; be it in person, on television, at work or passing in the street. On occasion I've had to converse with people who have strong accents and less-than-fluent language skills (credit to them; I speak no other languages beyond a very basic level). I conclude from this that in general, native English speakers are likely to be familiar with a diverse range of people speaking English and are relatively able to understand them*
My question is: For people whose native language has minimal adoption as a second language around the world; does this noticeably impede their ability to understand a foreigner speaking perhaps a rudimentary form of their language, when they encounter them? In other words, where encountering non-native speakers of that language is rare, does this necessarily mean that most native speakers will find them hard to understand when they are encountered, due to lack of familiarity?
If so, what can the second-language speaker do to mitigate problems in mutual understanding, if such a generalisation is possible?
(*on the other hand, I noticed that even west coast Americans failed to understand a word I said on the first pass in my more-or-less standard southern British accent when I visited, so perhaps high intelligibility of English is far from a given)