As others have pointed out above, phenotypes that register as "races" obviously have nothing to do with physical sensitivity. However, /social/ behaviors that we might associate with "races" might strike us as seeming more or less ticklish. This isn't a case of people from one society being any different in objective sensitivity than others, but rather that one society might encourage its members to express their sensitivity in a way that seems more "ticklish" to us than another society does. Ticklishness isn't so instinctive that it's unaffected by socialization.
Given the above, and based on my own, subjective and culturally-informed impression of what "ticklish behavior" looks like, I would actually say that people from certain Asian cultures (Chinese and Japanese, specifically) are socialized to act /less/ ticklish than those from, say, America. So to borrow the sort of charming, grammatically-incorrect phrasing of this thread's title: "No, Asian are less 'ticklish.'"
EDIT: changed a few words to hopefully make my sentences more readable