Yes, it does. You can see this by mouse hovering over that unit once its turn is over. You'll be able to see its main stats in the pop up window. And you'll see that its defense rating is higher, make sure to take note of unit's defense at start of turn (before moving or skipping turn)

So, what I'm getting from this is: Simply hitting the "pass" button to end your turn automatically sends *any* unit into "defense mode"? 

Or is this only for units that have specific defensive bonuses?  Either way, they probably should be more clear about this.

Any unit by default gains +5 Physical Defense if you skip or don't use an attack.  However there are traits that add to this +5 bonus.  Also, a fairly recent change is that the entire defending side starts in defense mode (even before their first turn in a battle), so even if you or the enemy are faster, the defenders can't be attacked without the defense bonus.

The only thing with regards to the defense bonus I'm not sure about is what happens when a unit spends a turn with a condition (like Dazed or Stunned, or even Prone) though.  It may require the turn to be purposefully skipped to get the defense bonus, or it may not.  Someone else will have to fill us in on that, or you can find it out for us.