Does orbital motion cause rotation? Assume the moon was flying freely in space, and not rotating at all. If if then happened to pass earth at just the right distance and velocity to fall into orbit, would its absolute rotation be altered in any way, or would its angular momentum (relative to the rest of the universe) remain at 0?
 A: In theory, Yes, when it passes earth at just the right velocity and angle - 
It would get some rotational motion due to the difference of earth's gravity between the far side of the moon and the near side. And due to the angle between the lines that join two sides to the CG of earth. That is what you need to rotate something. Far and near side means at different places on its circumference and diagonally opposite points.
If it was a point particle, then it would not gain any rotation because the angle between lines joining far side and near side to CG of earth would be same line, i.e. 0 angle.
A: A couple of points, too long for comment, but not meant as a complete answer.
Tidal locking doesn't mean zero angular momentum.  The Moon has angular momentum.  It rotates at nearly exactly the same speed as it's sidereal orbit, every 27.3 days.  The Moon is also unusually lopsided, it's near side being denser than it's far side, but I think we can ignore that aspect for your question.   Tidal locking requires rotation,otherwise, we'd see different faces of the moon as it went about it's orbit.   Tidal locking appears to be zero rotation, but it's not.
