I say no. He's determined that it's cycling on the evap temp switch and not low pressure
Undercharged, the evap is not going to get the stat cold enough to cause this
Either what he's seeing is normal.........how often IS it cycling.......?
Or likely the stat itself is going bad
More on the stat? Not much too 'em. Read your shop manual.......it's a cap tube stat that has the tube in intimate contact with the evap coil