I had a DV tape damaged 2 years ago after sending it through the x-ray. The week before the flight, I took a brand new tape and recorded over the whole thing (because I've heard that ensures there are no gaps in the time code). This proves the tape worked initially. The tape was in my carry-on and went throught he x-ray. On arrival, the camera rejected the tape. That was my only tape. When I returned home, the camera consistently rejected this tape and accepted my other tapes. So, yes it can damage it, despite all the claims to the contrary. It is possible that it isn't the x-rays but a magnetic field in the machine that causes the damage.
On previous trips I had always had it hand inspected.
I suggest you get them to hand inspect it. If you think the baggage screener will give you trouble, then you may want to put some film in a ziploc bag with the tape, and tell them you are demanding a film inspection.

P.S. I have never removed my camera from my carry-on.