Do you get any actual 'Irish-Americans' now? My London-Irish family used to be all of Irish stock - as the original immigrant communities (the 1950's wave I'm speaking of) would tend to stick together. But later generations get married & have kids with folk outside of the old Irish immigrant communities. Properly speaking I'm Anglo-Irish, but as everyone I know has some Celtic ancestry or Jewish or something - as far as I or anyone else am concerned I'm English.
To me 'faux Irish' would probably mean someone like me pretending to actually *be* Irish, rather than someone with a keen interest in their Irish ancestry.