737 'Wedgetail' already exists for the AWACS mission.
No need to re-invent the wheel - not that it would stop them from trying...
Different generations. Airframe is different, role is increasingly different, Radar is incredibly different - and would undoubtedly be multi-mode and underslung - and the vast majority of the processing and use would be distributed elsewhere.
We get back to the fact that even the 737 airframe is to big and a business jet would be more suitable.