Not exactly, it would leverage the Starlink technology, but it doesn't just offer secure communication, as the page says the current focus of Starshield is 3 areas: Earth Observation, Communications and Hosted Payloads. Note: a. Currently Starlink constellation doesn't do Earth Observation; b. the Hosted Payload could be anything, ultimately everything DoD wanted could be a hosted payload.
Whether this will be a service is not clear, I don't think giving control of the Starshield constellation to DoD is out of the question. It could be on-orbit delivery of satellites, and then train DoD personnel to use SpaceX built ground systems.
They built 4 prototype missile tracking satellites for the SDA constellation, I assume this is what you mean by "build to spec", but they told SDA they're not interested in doing this anymore.
"Build to spec" is not SpaceX's MO, they're more interested in coming up with their own spec and controlling everything end to end (i.e. vertical integration). Remember Elon's first step in design process is "Make the requirements less dumb", hard to do this in "build to spec".