I wouldn't trust them to do it for you. Let's face it they are swamped as it is so mailing home someone's knitting needles is most likely not a top priority.
That said there is another concern...does the airport have a mailbox? The first time I flew with my needles I took the padded envelope, correct postage, etc just in case. I asked as I was going through security if they had a mailbox and they said "no" so it wouldn't have done me any good anyway.
Last week when I flew to DC I made sure I put a lifeline through my project and just kept my fingers crossed. I figured the KP classics were cheap enough I'd take the chance. They didn't bat an eye. I do know of a few people who flew internationally and had theirs confiscated though.