If you're cranking at normal speed and the tach needle doesn't move up slightly as you crank, yes, I'd suspect the CPS....
EVERYBODY should carry a spare in the glovebox and the tools to change it (10mm 6-point, extension, breaker-bar/ratchet - all 1/4 is what I have, plus something to gently "pry" it out like a screwdriver)
It's located at the dampener end of the crankshaft on the passenger side, maybe 7 o'clock if you were looking from the bumper, back.
Next, pick a CPS to put in there -> Black, Grey, & Dark Blue Cam Position Sensor Perdels Test - Diesel Forum - TheDieselStop.com
What you describe is actually not typical of how they fail, and chances are, it's already been changed under recall (org was black, replacement gray). Usually they quit when hot and restart after cooling down for 10 mins or so, but anything's possible.
BUT, if you're stuck, get Anything
Even if it doesn't fix the problem you haven't wasted the money, because again, you should carry a spare so it's a good start