May or may not be armed, and yes a cruise missile would eventually run out of fuel. At that point it would either crash or self detonate. There would certainly be a record/data from any test firing of a cruise missile, but it's doubtful the military would want to advertise they had one go rogue.
To be clear, I'm not saying this was a cruise missile. I was commenting on the aircrew saying what ever they saw looking like a cruise missile, and extrapolating. There was a very similar story of an object matching this pilot's description crashing in Ireland 10-12 years ago. The conventional wisdom was that too was a cruise missile (either US or UK), but nothing was ever admitted.