Personally I would include it just so that the next homeowner doesn't curse you when they go to drill something into an expected stud that isn't there.

For a non load bearing wall, the biggest consideration is going to be hanging drywall which is why you'll see either 16" or 24" OC (to align with a 48" wide sheet). Since the wall isn't meant to hold any weight above it, there's a little more flexibility in where you place your studs, so you're probably fine without that extra stud.

That being said, check your local building code, there might be a regulation for that.