Despite packing it well, easyjet dropped my gf's bike wrecking a chain stay, a rear dropout, two chainrings, the bottom bracket and the pannier rack. It was her 10 yo trek so after much wrangling over how we'd waited to get home to unpack the bikes and discover the damage they bought her a Mercian. I escaped with a slightly bent front pannier rack that I can't be arsed to claim for.

If you do take your bike with them, pack it well and when it gets off the belt carry it to their desk, notify a member of their staff and inspect it in front of them. The frontline staff are usually OK but the claims department - WABOC.