I have traveled with various nieces and nephews both domestically and internationally, paying for my ticket with cash and theirs with points. It works as Mr. Tickets outlines, and I've never had any hitch. My one nephew was questioned in detail by a TSA agent. (Who is this man? What is your relationship with him? Where are you mommy and daddy?) Once, on KLM metal, we were separated when there was an equipment change, but when I brought it to KLM's attention, we were given three seats together on the bulkhead row. Other than that, no issues with having separate tickets.

Actually, IIRC, I've been able to get all the BPs online ahead of time.