Most military bases are in rural areas. Or at least used to be. ...
Let me start with this part first because that will be an important consideration to this discussion. What is urban and what is rural?
I was thinking about that point as I was recalling the various bases I have visited over the years. A quick trip down memory lane recalled the following:
Camp Perry
Fort Jackson, Eustis, Benning, Campbell, Chaffee
NAS: Millington (Memphis), Pensacola
Cape May
...and there may be others but that list should be enough for now.
I would consider all of these to be urban areas. I do agree with your point that when established, these areas may have been rural (or at least more rural) in nature and as the years have gone by, the growth in and around each of these areas has moved the area along the continuum FROM rural TOWARD urban.
We could disagree about where a specific installation may fall in that continuum (and how much it may have moved) but I think we would both agree there has been movement FROM rural TOWARD urban when considering the list above.
Considering we are no longer establishing new military bases, the transference of an area from more rural toward more urban is now limited to existing bases. This suggests to me the continued urbanization around existing military bases will continue to benefit those areas and leave behind more rural areas.
To be clear, I am NOT suggesting the military should build bases simply for the economic effect, but the latent (*) presence of the government (in this case, military bases) has and continues to benefit those areas in close proximity to existing military bases (which I hold to be urban areas). Another way of looking at this would be that rural areas now have one less way to grow (a very significant and powerful means by which to grow via the federal government).
* - just for the sake of full disclosure, I am referring to latent as defined by Robert Merton (Theory of Manifest Function).