Since the OP is international I can add one more experience. I am a junior and my FF account included it, so my boarding passes would always print LASTNAMEJR with the "jr" tacked on.

The jr is not on my driver's license or passport. Never was it ever questioned domestically by FAs or TSA in any way.

International was a different story. No experience with Italy, specifically, but it has resulted in me being pulled out of line upon boarding in SIN, NRT and AMS on different occasions last year. In all cases I was asked my name, where I was coming from, going, etc. but in all cases was allowed to board after not more than 5 minutes of extra scrutiny - it was certainly not fun, though! It was easier to get the FF account to match the passport than visa-versa so I have now had the JR removed by sending in a photo copy of my IDs. (Plus, I have higher status than my dad now anyway!). Flying back from LHR after this was done resulted in no extra scrutiny.

I would say that your friend with *probably* be ok and eventually be allowed to fly but it will *likely* result in some questions departing from overseas. It depends on your level of tolerance for being questioned in foreign countries on what you'd like to do.