It seems extremely unlikely. As far as I know, they aren't doing dialogue tags for the Background because that would be too much additional stuff to do, so ambitions/aspirations are certainly also too much.
There are 13 backgrounds, so it would not be practical to give dialogue to each of these. HOWEVER, there is a different way to approach this. Mass Effect 1 did an excellent job of giving your character a backstory based around a single event and how your character handled it. Basically it was a famous battle that people knew about and you picked if you were the hero or tyrant of that battle.
Doing something like this for BG3 would allow Larian to create only 1 background for custom characters involving some kind of event. "Oh, you were the person at Baldur's Gate when X happened." That gives one story for a custom origin. You then answer questions (such as telling things to the tadpole like suggested earlier) to define how YOUR custom character interacted with that event.
So, 1 origin for all custom characters that you then define for yourself. Even with multiplayer, these can make characters somewhat individual. Each define for themselves how their character responded to the famous event, and the world responds to them in kind. Otherwise all the unique interaction goes to the gith and drow (or Origin characters).
