Upvote:2
As @greyshade commented, I don't know what you might be worried about. I've bought tickets for parents, kids, boyfriend and they all worked fine. Admittedly, those were all domestic flights, but I've had international tickets purchased for me by my employer.
Definitely try to access the ticket record via the confirmation number on the British Airways site (BA) before check-in time. They may allow you to pre-enter passport/visa information/contact information/enable alerts/etc.
If it is an international flight, you might be able to check-in but not print boarding passes. At least in the US, they want to see your passport etc. at the ticket counter.