No, you don't need the work mode engaged to mow. The work mode simply lets the operator have more control for finesse work or when less initial response is desired when operating the foot control. Useful if you want to make slow movements with the machine as the pedal is initially depressed. On my D series, the work mode results in a more abrupt stop if I let off the foot pedal rapidly. The standard mode gives just little roll out when I release the foot pedal and a slower stop. I prefer the latter when mowing.
The top speed of the TC in the work mode or normal mode will be the same when the foot pedal is fully depressed -9 mph on the D series in nonrabbit setting. Just the initial response is different with each mode.