Can I connect this to my exiting Jacuzzi tub in my bathroom?

No. The pump itself needs to be installed at the water heater and the sensor valve needs to be installed at the sink furthest from the water heater to ensure optimal operation. If your goal is to get hot water to the Jacuzzi faster, installing the valve at the sink in the same bathroom would accomplish that goal as long as the pump is correctly installed at the water heater.