Germany has always been a "jus sanguinis" country, meaning that the basic principle of its nationality law is blood descent. This stands in contrast with "jus soli" countries like the United States where the basic principle is place of birth. A child born in Germany is not automatically a German national. It used to be that birth on German soil was completely irrelevant to questions of nationality, but children born in Germany since 2000 can acquire German nationality by birth if one of the parents was a long-term permanent resident. I question whether a military baby would qualify, as a soldier stationed in Germany would presumably not be there under a German permanent residence permit.

Assuming for the sake of argument that your son did have German nationality, he would certainly be subject to the draft - if it still existed. Germany ended compulsory service last year. But this does point to a larger issue: anybody with multiple nationalities is fully subject to all the legal obligations imposed on citizens of each country.

(I am not an immigration lawyer, but I've sent a lot of time researching nationality issues. I've also spent some time in German embassies: I have a German wife and a child who is therefore also German by virtue of jus sanguinis.)