I don't see why it wouldn't work, although it would almost certainly raise the temperature of your GPU water loop. Either that or you'd need a huge heat exchanger to move much heat with only a few degrees deltaT.
No you just need a water-air heat exchanger to provide supplemental cooling downstream of the hot tub heat exchanger.
GPUs ---> Pump ----> Hot tub heat exchanger ---> Water/Air heat exchanger ---> back to GPUs
Would you though? If it takes x amount of watts for a hot tub to maintain temperature of y with it losing heat to evaporation/convection then so long as you input x or less watts then your water temperature won't exceed the original design. Issues would arise when you add more than x amount of watts to the water in the hot tub. Then the temperature would rise until the increased delta t between the water and ambient air caused an equilibrium to be reached through evaporation/convection. This isn't an issue for a heatsink but it is an issue for a heatsink that humans would like to enjoy sitting in. In that case then it would make sense to run a water/air HX before the hot tub so that you add less than x watts and then supplement to reach x watts.
No that would be bad. Heat exchangers work better with a higher Delta T. Cooling the water before getting to the hot tub would make it useless for transferring heat into the hot tub. If temp is less than hot tub heat would actually flow to the GPU loop. If the temps are close you would get minimal heat transfer. Also you have little control over how "cool" you get the water. Lastly the temps leaving the heat exchanger will be close to the hot tub temp. So your "cold" input temp for GPUs will be 60C-70C. You are cooling the GPUs with water higher than the temps you want them operating at.
Pretty simple to solve the "humans don't like it that hot problem". The first is that the hot tub will never get hotter than the GPUs. If you use something like cgminer to throttle GPUs based on temps then water in loop will never be hotter than the temps humans like. If you want max GPU temps then you need a bypass valve. If hot tub is < desired temp then water flows through heat exchanger. If it is >= desired temp valve closes and water flows around the heat exchanger.
GPU (60C) -----> hot water heat exchanger (drops temps to ~ hot tub temp say 55C) ----> air heat exchanger (50C) ----> water returning to GPUs (50C)
GPUs then heat water back up to 60C and the cycle starts over.
I suppose I should have used real temperature examples instead of abstract values. In my case I meant if the GPUs and hot tub started at 25C and you were adding more watts than the hot tub could dissipate that the water temperature would climb until an equillibrium was reached. So, if at some point your equilibrium is achieved at 87 Celsius, you could dump an unknown amount of watts before the water hits the hot tub so that your hot tub achieves a comfortable temperature. This way you don't throttle your farm(I mean we're here to make BTC, not heat a hot tub, right?) and you keep the humans happy. Hell, you could use a PID controller on the air/water HX to control the fans such that the outlet temperature of the water before it hits the hot tub is at the temperature you want the hot tub.
It would also appear that hot tubs run at around 60 Celsius. So, if your GPU inlet is 60 Celsius then you are looking at GPU temps around 75 Celsius which isn't half bad. You can't dramatically lower the inlet temperature unless you also dramatically lower the flow-rate as otherwise you won't have the time to heat up the water going through the blocks such that your outlet temperature is higher than your hot tub temperature.
Pretty interesting discussion. Would be fun to run a stirling engine from your waste heat to power the fans that provide cooling in a more traditional watercooled setup.