The fact that this logo is close enough to the fictional utopian UFP logo I am sure was considered. If not, all involved are not even as intelligent as a bag of meteorites.
Associating a war-related agency with such a positive legacy of our culture as Star Trek and all its iterations was without a doubt considered, but was used with a very easy and an entitlement with past military space-related logo symbols. Sure the artists for Paramount's Star Trek in designing the symbols for the series likely looked at the military designs and for believability for the series and designed with those in mind. When imagining an Earth's future utopian culture, creative designers would take a logical and believable association from the past. So maybe you could say the Paramount artists naturally designed with the military's designs in mind. It would make an interesting copyright court case if challenged.
I, however, cannot for a second believe this was not understood by those in the government agency art-creative direction positions and seen as an easy association to be used for the subtle optic advantage and cultural worldwide influence it would have in framing a purely military and defense branch. Not though for the exploration and search for extraterrestrial friends and positive advanced human endeavors the fictional United Federation of Planets were designed to represent. Optics for media today now are considered for everything.