I think we're more likely to see some splitting of timelines shenanigans, where we find out that we (the viewers) are following only one of the Doctor's timelines but other versions of the Doctor continue to adventure in other timelines. We had the 13th Doctor straddling universes in Tecteun's timeship, hinting at parallel universes. In the recent Tales from the Tardis episodes, we saw older versions of past Doctors, with the 7th Doctor muttering something about different timelines as an explanation. And in a recent Doctor Who Magazine, Russel T. Davies has claimed that The Giggle will reveal "a whole new way of looking at the history of Doctor Who" that could be quite controversial. So my money is that we get to see both a timeline where 14 regenerates into 15 and one in which he doesn't, with the implication being that there are also versions of previous Doctors who didn't regenerate when we thought they did and have gone on to grow old and have other adventures.