Yes, they do. Sony may have less available than Microsoft (I'm not 100% on the actual numbers), but they do have them and just like Microsoft, they leave it up to the developer to use the servers if they want to. For example, CoD's developers do not use them for their games (to be fair though, they did use some for PS4 and Xbox One versions of Ghosts, but those versions of CoD still do not run completely on dedicated servers).