This has to create a paradox
If Doc Brown never pursues science and so never creates a time machine, none of the events happen that allow him to go back in time and convince himself to do that. So he'd end up creating the time machine anyway ... and it would create a kind of loop.
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As we know, there's always a way to fix those loops.
Yea, I guess you have to suppose that the characters from the original timeline are operating in bubbles that aren't affected by changes in the timeline until their event horizon expires and they disappear. And they remain in the timeline as material to other people for as long as they don't disappear, as traces of the original timeline.
That would make sense all things considered, I guess.
Although what's would happen to Marty? If he managed to return to the future he'd have a double there.. so he'd either have to stay in the past, and the Delorean would disappear, or he himself would disappear. I think the latter is more reasonable.
So maybe it would come to a choice between the current Doc, First Citizen Brown, disappearing, or Marty disappearing. ! Would the Doc be that selfish if it were the case?
if you believe in the deleted scene from part II of biff disappearing when he gets back to the future, that would create a paradox. But if left alone, the timeline would show an older version of biff from a different timeline show up in 1955 since he doesn't live to the year 2015 in that timeline.