After watching mine fall off a baggage cart and roll across the tarmac, I suggest taping something to the PVC tube so it doesn't roll. For next time, I thought I'd make an arrow case to match and tape them together.
And cross my fingers? Actually, I think shipping the bow ahead is a better idea these days. When I did it, there was no extra charge for baggage. Might as well ship most of everything else too, and not have to deal with carrying it through the airport.
Be careful if you decide to ship a bow case empty for any reason. Dan Quillian was investigated for fraud by one of the shipping companies because he would occasionally ship an empty case to someone for returning a bow. They assumed he was going to claim there was a bow in the case and file for a loss. Guilty until proven innocent!