Happened to me last September and the BA staff in UK didn't bother and checked me, wife and baggage all the way from EDI, via LHR to LAX where AA promptly declined to let me accompany my bags to LAS for the last leg. The end result was a two and half hour wait, £42 phone bill to BA to fix the issue and re-issue tickets, and stratospheric blood pressure ��

I now wouldn't contemplate travelling without checking them first as, afterwards, BA pretty much threw a couple of thousand AVIOS at me and said tough (yes, I'm still out the £42 too ��).