Well, that's assuming the questline was designed around the assumption that you were Dragonborn. Which... starts to get into some complicated issues between game design and lore implications.
There's also the issue of the fact that... Well... We still don't really understand exactly how Souls work in TES. If this was, say, Warhammer 40k, i could give a very precise account of the function and interaction of the Soul, what happens when you die, and exactly what makes it up... But with TES, we've got all kinds of seemingly conflicting information, from Sithis being the inevitable oblivion of all souls, to the Nightengales indicating that souls eventually fade away, to the Soul Cairn, to the Dreamsleave and its recycling, to Lysandus indicating that souls can relatively easily travel from Aetherius to Nirn...
There's a lot of unknowns, which ultimately makes any conclusion somewhat shaky.