Do Barbarians ever pillage AI's irrigation?

[colossus]

It happens to me that mounted barbarian units always pillage my irrigation if where they land is not immediately next to my unit or city.

But I have never seen a barbarian unit pillaging the irrigation of AI's territory. Is it true?

[Prometeus]

If barbarian units has Alpine abilities, of course they'll pillage AI's irrigations...

[Smash]

I'm not sure if actual pillaging does take place.I know they will attack and capture ai cities.Most of the time I see barbs sitting in ai forts doing nothing.The cheat menu would provide the answer.