Maybe, that's why they have FOD walks, but then again the F16 wasn't flying so it didn't actually bring it down - which seems to be the theme of this thread -. But its highly lightly if they knew something had been injested, then as a mater of course it would have been shut down and inspected , although I find it hard to believe a plastic cassette tape 'trashed' a complete engine to the point it was trash.
But I wasn't there so who knows.
Luckily this Chinook was build of stronger stuff than that F16 or the Chinook were talking about here
What's So Special About This RAF Chinook? | Fighter Sweep
Although after 30 + years of surviving war zones, who knows maybe it will finally meet its end at the hand of someone armed with no more than a mavic drone - or maybe even a plastic video cassette ;-)