Not really. A city is an administrative area, yes, but depending on where you are in the country the role you are describing might be a "township." In addition, there are often qualifiers to be a "city" in most states. Most cities end before reaching rural areas and you get into a township or "just a" county; we generally refer to "rural" as not in a city in casual conversation. Urban is different and not necessarily the direct antonym of rural; there's a middle ground.
California seems to be an exception where my GPS will report a city quite far away as "where I am now" when I'm in the sticks, but that might be my GPS. California is also less particular about administrative division naming than, say, Michigan.
City, town, village, county, parish, and township all have particular meanings that vary across the country. This is not an area where one can say "the USA" and be correct, as with many things in our really-50-countries patchwork. One example is that Wisconsin dubs "towns" what Michigan calls "civil townships."
America is confusing, even before you get into the debate over New Urbanism.
California is quite peculiar. California has 482 municipalities. Whether they call themselves cities or towns is local preference, although fewer than two dozen call themselves towns. The largest municipality is Los Angeles with 3.7 million people. The smallest is Vernon with 112 people. I live in the unincorporated town of Cambria with a population of about 6000. We are about 20 miles from the nearest city, but we have no local government at all. The closest we have to a government is the community services district which runs the water district, the sewerage treatment plant and the fire department.
Cambria is in San Luisbo County which has an area of 3600 square miles and a population of over a quarter million but only 5 cities. California has a law that makes in almost impossible for a new city to incorporate. The new city must reimburse the county for any lost tax revenues caused by incorporation. If your GPS reports a city some distance away, it probably reporting the county seat of an unincorporated area.
California seems to be an exception where my GPS will report a city quite far away as "where I am now" when I'm in the sticks, but that might be my GPS. California is also less particular about administrative division naming than, say, Michigan.
City, town, village, county, parish, and township all have particular meanings that vary across the country. This is not an area where one can say "the USA" and be correct, as with many things in our really-50-countries patchwork. One example is that Wisconsin dubs "towns" what Michigan calls "civil townships."
America is confusing, even before you get into the debate over New Urbanism.