"Faux-Irish" may well be a bit insulting - I might get a wee bit miffed if I was called that.

Pride in one's heritage doesn't make much sense, however. The great George Carlin had a rap about this; he said something to the effect of "Why would you be proud to be Irish? It's an accident, not an achievement. Might as well be proud of having brown eyes, or type A blood."