I think that given the right circumstances, any group of human-beings can migrate anywhere if they need or have to do it. After-all, a small group of homo sapiens left Africa around 140,000 years ago, and eventually populated the entire planet! I mention this because there are three issues of Hakka identity that are curious to me, 1) recurrence of blond hair throughout Hakka-Chinese populations, 2) Hakka women are equal to Hakka men, 3) Hakka women never had ‘bound’ feet.
However, again I am of the (as of yet unverified) opinion that a ‘high’ percentage of this small amount of European DNA probably occurs in an unusually ‘high’ amount amongst Hakka populations. This is all speculation on my part, and more research is required.