Does waiting change what the event will be at a "Distress" beacon?
Well, the only people that can 100% reliably answer are the developers (or anyone who might have decompiled and reverse-engineered their code, I guess).
Having said that, my totally anecdotal evidence is that I have seen negative distress beacons very early and helpful distress beacons very late in my time in a sector. While it's an interesting (and logical) theory, I haven't observed any patterns leading me to believe it's implemented that way.