I'm pretty sure it does create new ones. The main reason I noticed is that the filter for Design Backup Servers on the Galaxy Map will know they're there, if you've previously explored a planet, but haven't revisited the planet since the Server showed up(e.g. you decide to unlock Mark IV Scout Starships at the beginning and map out the whole galaxy in advance).
I remember being confused about the map filter telling me there was a Backup Server on a planet, but all the old planet data showed no such thing. I sent ships to revisit the planet, and found there was indeed a new Backup Server where there was nothing before.
I don't know how random it is, but I'm pretty sure you wouldn't get 'free' designs from having multiple Servers on the same planet, just as you don't get 'free' designs from planets with multiple fabricators. Well, in the latter case, you do save time(as it's all in one hacking 'session'), and I believe you're simply charged for multiple hacks at the same 'current' price, compared to having the price rise after each individual hack.