Oh yes. I would punctuate it as "Do you, by any chance, happen to speak English?" The tone of the question implies that the person is not expected to speak English, so it is considered a polite way to ask, as opposed to something like "Don't/Can't you speak English?" (which would be very rude)
I use this construction all the time if I don't want to bother someone but I need some information or help. "Do you, by any chance, happen to know in which direction the Museum of Modern Art is from here?" "Do you, by any chance, happen to have change for a $5 bill?"
The idea is that it would be a fortunate coincidence if they did but you don't expect them to do or have whatever you're asking for.
Some Americans are more direct in their speech and wouldn't use this kind of indirect request. I'm not saying that all Americans use it but it's certainly very familiar and very common.