I don't think the show has indicated either way whether the staff speak English or not, but historically Ragni (Martha's lady-in-waiting) did speak English (and French, Swedish, Norwegian, and Finnish). (She grew up in Finland with Norwegian and Finnish parents, went to Swedish schools, and traveled extensively in France and England as a teenager.) So yes she definitely could have understood White House staff gossiping in English. :-)
I'm a Scandinavian royal history nerd. ;-)