Just to be sure, I would still check with an actual commercial HVACR pro and not go by what the maintenance supervisor or anyone else says.
It sounds like you have a decent customer that wants to spend some money.
If you don’t happen to do a lot of this kind of work… her is just my 2-cents worth.
With HVACR today, it is all about system efficiency.
On some systems, those cooling tower pumps do not need to run when the chiller system temperature controls are satisfied and the chiller is not running. They are normally only for the purpose of heat transfer from the condenser and are not part of the chilled water supply loop, which feeds the fan coil units throughout the building. If the system is operating properly, the lowest leaving chilled water temperature should be around 40 degrees F, so evaporator icing should not be a concern. Many times, those pumps are at least 15HP. If they are not needed and are running 24/7 they are probably wasting electricity, reducing overall system efficiency and causing the need for more city metered makeup water for the tower as well as more on-site water treatment chemical injection, if present. You could come out smelling like a rose by both picking up the extra associated control wiring and helping them reduce their annual operating expenses if you team up with a qualified commercial HVACR pro.
As I said though, just my poopy 2-cents worth!