I've also wondered about this for many years, but have never done any calculations to see if it's feasible. But thinking about in superficial terms, I think it would be. Supercharging definitely works, but I'd bet the first guy to suggest it was laughed at because others said:
"Why would you want to waste power from the engine to drive an air compressor? It won't make any more power because the compressor will absorb all the extra power produced."
We all know that is not the case. Engines make useful power because they burn fuel, and the air that is required for burning that fuel is relatively easy to manipulate for temperature and pressure. I think the fundamental question to be answered is:
"Will the system for refigerating the charge air absorb more power than is added by burning the additional fuel enabled by higher intake manifold density?"
Unfortunately, I don't know doodly-squat about how much power refrigeration systems absorb for a given amount of cooling and mass flow. But I can give some ballpark numbers for engine airflow conditions. Let's say that we have a 2.0L turbocharged engine running 15psi boost with a 90% effective intercooler on a 77F day. At 5500 rpm and 30% thermal efficiency, the engine would produce 302 HP. The heat rejection from the intake airflow of 1600 lb/hr would be 1011 BTU/min.
Then add a refigeration system to the intercooler loop with an assumed media temperature of 30F, and keep the same assumptions for engine performance as above. Intake mass flow would increase to 1732 lb/hr, and intake air heat rejection would increase to 1387 BTU/min. Power would increase to 327 HP just by decreasing the intake manifold temperature, an increase of 25 HP. I don't think that a refrigeration system would absorb all that additional power. Are there any HVAC engineers out there that can ballpark some numbers on the refrigeration system?