Both the Templars and Assassins are now aware of The Ascendance Event, it is when specific bloodlines converge together throughout time, and they all usually meet up around a Piece of Eden. So there is a connection, the explanation given that it is from Sub-DNA - which constitutes the collective unconscious of the human race. The 'Last Descendants' contain the entirety of the Sub-DNA code between them, which in theory means they could access it via an Animus.
One of the explanations provided is that it is related to the theory of the collective unconscious mind. This was a theory created by Carl Jung who summed it up as follows;
"The collective unconscious comprises in itself the psychic life of our ancestors right back to the earliest beginnings. It is the matrix of all conscious psychic occurrences, and hence it exerts an influence that compromises the freedom of consciousness in the highest degree, since it is continually striving to lead all conscious processes back into the old paths."
The work of Sebastian Monroe discovered that within all humans there is what he coined Sub-DNA. This is a separate code hidden beneath the primary DNA, that is only found in select humans, but possibly was part of all humans at some point.
The phenomenon has only beendocumented a handful of times in all recorded history, and is not wellunderstood, governed by sympathetic genetic forces we’re still decoding. Thatwas actually what Monroe was working at Abstergo, with his modified Animus. He was researching these Ascendance Events, looking for the next occurrence.