The short answer is "YES".
It sounds like you understand the situation better than most of the folks ho are offering answers. In fact, my understanding is that it's one (if not the MAIN) reason that the ethnicity percentages that they give you in DNA can be wildly inaccurate. The fraction of DNA you get from your 4th great grandparents is not EXACTLY 1/64 - that's just an average. If you go back far enough, some of the fractions can become effectively zero.
A legitimate point is being brought up though is about the relationship between genes and ethnicity. Realistically, certain genes will be more prevalent in various "gene pools", so it's kind of a minor, nit-picky point. A better issue to bring up in that regard is the possibility that somebody born in Germany might not be German, ethnically. Maybe the person's grandparents migrated to the town from Poland, or someplace, for example. So a "German" might really be Polish, ethnically. I wouldn't say that's a particularly serious concern, though - just something to think about.