It's definitely possible to combine this with some sort of "co-generation" scheme, where either the heating or cooling are combined with e.g. energy flowing off

It's definitely possible to combine this with some sort of "co-generation" scheme, where either the heating or cooling are combined with e.g. energy flowing off of a data center. However -- for this to work as described (hot air spins a turbine), you need to get a much higher temperature differential than would be typical for data center waste heat. You'd still need to concentrate that heat somehow into a high-temperature reservoir (think hundreds of degrees Celsius) to have it be space- and energy- efficient.