That's incorrect. The two are separate procedures and serve separate functions. Every airport with an instrument approach is evaluated for a diverse departure, to see if the obstacle and terrain permit it. This allows you to climb and not hit anything if you follow any limitations in the diverse departure, regardless of whether it complies with an ATC clearance or not. It's evaluated to 25 or 46 nm from the airport. Typically there is an airway within that distance, though in some remote areas that may not be true. Radar coverage is not required or considered.
A diverse vector area tells ATC what range of headings they can assign on departure in order to get the airplane to their MVA. It's very much an ATC function, and these are developed in coordination with ATC and consider their radar coverage.
So, you will have a diverse departure (or at least an evaluation of one) at every IFR airport regardless of size or ATC services. You will only have a diverse vector area at larger airports that have the radar coverage to support it (and the need for it - note that none of the NYC airports have a DVA, for example).