You couldnt do it without publicizing. Space stuff is big and loud. Space itself is transparent. Doing big secret stuff in space is extrodinarily difficult.
You can't hide that your about to do something in space because launches are loud and obvious. However, once in space, you can absolutely hide what you are actually doing. We still don't really know what the Air Force Space Plane does while in orbit.
There are spy satellites that we know nothing about in orbit, only until someone like Trump leaks an image on twitter. Who is to say where that line of development ended, if ever, given so little is spoken publicly of these efforts? Perhaps others could detect some of your efforts, but you hold them to secrecy like you do other state secrets among allies out of mutual benefit. I'd expect there to at least be a well worked out plan for such an infrastructure along these lines by now, if not implementation. It's one of those things where the losing move is not to engage with it, for fear someone else is and making strides.
Except we know when they were launched, thier general orbital parameters, and what they are generally doing. We dont know the specifics but their existance as spy sats is well understood. There is even an online community of enthusiasts looking for and tracking them. Wikipedia is full of data.