You will have the same concentration of alkalinity in your cooling tower no matter what raw water you use. Assume that you are controling your alkalinity to 200 mg/l
If your raw water has 50 mg/l of alkalinity, then you have 4 cycles of concentration. Blowdown is used to control the concentration.
If you treat that raw water with an RO unit, then you will have approximately 5 mg/l alkalinity in the treated water. With RO treated water, that would allow you to increase the cycles to 50 cycles of concentration and decrease the blowdown flow.
This is just a hypothetical discussion. Note that cooling tower alkalinity is usually controlled by adding acid.
I understand that hardness, alkalinity, and silica are the main control parameters for cooling towers.
Generally the makeup water for a cooling tower is of lower quality and RO quality water is too expensive for use in a cooling tower.