Well, I'm sure there are as many answers to that as there are people and situations. Some native English speakers may have no experience with foreigners and have little tolerance for trying to communicate with someone with poor English skills.
But I think a lot will appreciate the effort and try to be helpful. You may not chat about current events, but if you need to ask something you'll probably find success.
I deal with foreigners in my line of work often. Believe me, their English, even if poor, is a lot better than my Spanish, Portuguese or Japanese. If they don't try to speak in English, there is going to be little communication at all.
Sometimes the grammar and phrasing is not the best, but I can usually understand what is being said or written.
Oh, and some people here do try to pronounce ASAP as if it were a word, but they are usually thought of as pretentious.