It is really up to the local tsa to decide, but local check-in staff would follow local rules.

LHR's CX check-in staff asked me to check-in "long umbrella" as a hold baggage, citing tsa would not let me bring it through security.

So when I bought a long umbrella in Japan, at NRT, I was naturally expecting check-in staffs to ask me to check-in my umbrella as hold baggage, but they smiled at me and said, there is nothing stopping me to carry a long umbrella on to the plane myself. They were correct, NRT tsa didn't say anything at all.