After hearing about this theory I went back and watched The Door again, and I have to say the parallels between Bran's body in the present and the human night king's body in the past are pretty provocative. And again, when Bran goes back alone, in light of this theory it's easy to imagine the army of the wights who can't see him as the ranks of an army formed up before their leader (Bran). So, I think there's definitely something happening here, and some much deeper connection between Bran and the Night King than the mere fact that NK and the three eyed raven are both ancient beings of Westeros. That being said, almost all the side-predictions in this seem far fetched at best, and at worst wholly unsupported by any evidence from the series or the books.

For me, this theory really starts to fall apart when we revisit Brynden Rivers death: Before telling the three eyed raven to leave his body, Brynden Rivers deliberately instigates the whole Hodor fiasco. As Meera's shouting about Hodor and the whitewalkers, 3-eye tells Bran "listen to your friend," i.e., warg into Hodor, from here. He does this presumably to teach Bran some lesson about the nature of his powers/set in motion some path that ends in the defeat of the Night King, not set Bran on to a bungling series of time-travel adventures a la Bill and Ted, that ultimately result in his becoming the Night King. And anyway, Bran can't do that stuff you say. While he does warg into Hodor from the past and affect past-Hodor, he doesn't warg into past-Hodor and control him, or affect the past in any deliberate way. To the extent Bran can change the past, he can in a roundabout and inexact way, and he does so under the guidance of the 3-eyed Raven. The same all knowing 1000 year-old greenseer who has told him, from experience, that the past cannot be changed. At best, Bran could conceivable greensight back to the creation of the night king, warg into present tense night king, and give the human who was about to become the night king a stroke, thus rendering him an unsuitable candidate for conversion.

TL;DR: we have no reason to believe Bran can affect people in the past with anywhere near the precision this theory would require.