No you don't have to add an overload. Sorry code book is not handy but section 28 does mention thermally protected motors.
Yes, in regards to overheating, which is not required on motors that don't need overload protection. (28-314 / 28-318 / 28-302) Am I missing something?
I think the confusion is about a $50 motor protected by $150 of overload devices.
Unless the Electrical Engineer on the jobs askes for it and, of course, you haven't put that into your estimate! Heck he'll probably ask for a NEMA 4 enclosure, hand/off/auto, push button off/on, and a min. of 1 1/4" EMT conduit feeding it! (crazy yes, you never know with EE)
