Electricity like water will always follow the path of least resistance. So yes, just grounding the mast would suffice.
However, IMHO I would start the ground at the last solid piece of the J-pole and run the ground down the mast and continue on into your ground rod with minimal angles in the ground wire.
I did this on my J-poles and additionally added a seperate ground line for the mast. Yeah it's probably excessive and redundant but I figured an ounce of prevention/protection. Plus if for any reason the connection between masts wasn't 100% it would give the static electricity an oppourtunity to pause and possibly change direction. Like down the antenna cableing.
Additionally I made 4-5, 5-6 inch loops in the antenna cable at the bottom of the masts then again just before entering the house.