Getting raided is not the issue, but in any case you will have the right documents.
You will be checked; the Q is whether they just check you and your papers and peek inside the plane (I’ve had that many times, anywhere, even once with a dog sniffing all inside, at LIMW) or throw the entire content of your plane outside (in the rain perhaps) which has been done in Italy specifically to N-regs. Overall very rare though.
It is other issues like A&P/IA availability etc – plenty of threads. Not many people are going N-reg today, for various reasons.
You will need FAA papers to fly an N-reg outside your country, in addition to EU papers.
Identical threads merged.