The problem is, if you feed cold water into your normal heating pipes, all the piping and radiators will get wet from condensation. So you would have to have a regulator that measures air moisture and temperature in all your rooms and only feeds water with a temperature above the dew point. This is possible, but inefficient and (especially on hot+wet days) doesn't cool very well.
The possible real fixes are either to section off your water circuits in summer, and only run the properly cold water through FCUs, wall or ceiling loops.
Or to get a multisplit heat pump, use a normal refrigerant-air indoor unit to cool and a refrigerant-water indoor unit to heat the water loops.
Yeah, I wasn't planning to run the cold loops through the existing radiator piping. I just want the ability to cool at least 1 room by reusing the air-to-water system, even if that means the FPU requires its own piping from the outside.
In that scenario, are FPUs a good option? Are there other drawbacks?
Most Francoils I know don’t have a way to get rid of any condensation that happens in the unit like internal air conditioning units do. So even if you run the piping outside of the house you have condensation in the unit and the floors, not to mention the walls.
Even then, there is a fair limit in cooling and efficiency you can get from them because of the lack of phase changes occurring.
If you have a balanced mechanical ventilation (both inlet and outlet) that would be one of the best options to condition the whole house without putting air conditioning units everywhere. Having said that, we turn on the air conditioning in the attic during hot days which removes the biggest heat and moisture from the house. Next up is installing more sun blinds to prevent the heat from entering in the first place.