Depends where you have added the files to your media player from. And do you mean the LW media player or WMP or similar player?

If you added them to WMP's playlist whilst they were in LW's download folder, then yes they will disappear. And if you delete them then they will be gone forever from your computer unless you copied them somewhere else on computer.

I recommend moving the files to My Music folder ... adding them to WMP or other player's playlist. And sharing that folder back to LW by choosing that folder under LW's menu bar, Tools > Options > Sharing.