I ran into this problem getting a license in MD - the second time. The first time, the guy said it was no big deal that I didn't have it and sold me a license. The following year, a different guy explained that what actually happened was that the guy last year checked a box which essentially said that I had completed the HS course, but since I couldn't provide proof at the time of purchase, I would carry the proof with me while hunting. Further, if I didn't have proof on me and I was stopped, it would be considered hunting without a license and I could possibly have my gun and truck confiscated. Wow - wish I had known that the first time! I went home and found an old wallet, which luckily held my hunter safety card from 1991.
I remember using the HSC to get my first license and, from then on, using the previous year's license to get the new one. Up until PALS, of course.
To answer your question about the certificate, I don't know. I don't recall getting anything other than a card and an orange hat after the HS course. Maybe in Missouri they issue a "certificate" instead of a card? I only had to show my card, which does not have any number on it, so I'm not sure what the selling agent recorded in my case.