I quite like Yoodie. I don't think it would be a problem to have a shipboard AI, especially if it is used as an explanation as to why they aren't used much. I can think of several reasons that would be the case, such as the fact that central computer systems can easily be rendered nonfunctional by way of a computer virus, like in Battlestar Galactica.

My only major worry with this story is that it may be a bit confusing for audiences at first, but if as you say it is intended to be seen after the OT, then that probably isn't so much of a problem.