For the most part yes, although any temp reduction of the water going in compared to the car will be a direct offset- so a small improvement to be had. The issue is not the cooling, it is getting the heat from the copper to the coolant and that is not something you can solve easily. The biggest problem of any induction motor is cooling the rotor, there is a pic on Reddit of a Tesla rotor that has reached over 400degC as it is purple color in the middle.
You can move the inverter to a separate coolant loop which will help a little- OEM the motor pre-heats the inverter coolant so it isn't a particularly good design for high power.
The later Y/Plaid magnet motors would be a better shot as they have a much better coolant system, however they aren't as easy to implement as the LDU since there isn't a drop-in inverter option yet. There will be one coming though, somebody will hack it for sure.