No.
Typically, all a media player does is just play the file, i.e. get the file handle from the system and read from the file's data. In most cases, data is even pre-cached from the disk into main memory, so playback isn't affected by disk access from other programs, and your hard drive won't always be read from.
Anyway, a media player typically does not write to the file, which means that your file won't be touched. Even if the process quits unexpectedly (for example by force quitting it), the operating system will just release the file handle.
You can even test that. See if any of the file's information changes (e.g. timestamps, "modified" time) when you play it. No decent player should do that without you actively changing information and pressing a "save" button. There are some players that behave differently though.*
* For example, iTunes will automatically update ID3 information in MP3 files once you change something in the "Info" dialog. This is in my opinion not how it's supposed to work, but these file saves only happen once, which means that you most probably won't just "lose" a file if something goes wrong.