Not really. The media player already updates its UI only when it's really necessary (as you can easily see when switching from/to the media player in the task switcher or when locking the screen). It does (or should do) "nothing" when playback is paused/stopped. A sleeping/blocked process does not take any CPU cycles. It just takes up main memory.

Also, stuff like MAFW (the backend that is responsible for actually playing the media files) keeps running in background (again, only taking up memory, not CPU cycles) even when the "Media Player" (the UI) is closed. You can check this with "ps ax" on the command line. (This is also the reason why Media Player and the Browser start up that fast - parts of them are kept in memory, sleeping and waiting to be activated.)