From what I know, mostly from War Room, positional needs definitely play a significant role in the picks they make, as Belichick requires his scouts to make the case for who the prospect will replace, both short and long term, and that goes into how they rate them. But they don’t stack the board by need, e.g...1st round OL, 2nd round TE etc etc.
I also believe, from everything I have heard over the years, that the Patriots actual draft board is much smaller than most, a few years ago I heard they had fewer than 40 players total on their draft board. I have no idea whether that is actually true or not, but if it is then I think they also keep track of players who are dropping on draft day who they may have thought they had no chance at. Wilfork being the best example of that, but also Malcolm Brown a few years ago.
In short, I don’t think they will take an OT in the first round if they don’t have a first round grade on them, and if their board is devoid of players with first round grades when their pick is coming up then that’s when you see them trade back. However, on rare occasions, if they see a prospect they really like and need they will move up to get them before another team can get to them, with Hightower and Chandler Jones good examples of this.
