Listening to Music can Enhance the Productivity of a Person while Performing a task?
Yes, it can. Especially video game music, because it's designed to be played softly in the background and keep you engaged in what's going on.
Best advice I ever got in this regards is to make two playlists, one being 'field music' and one being 'boss music'. Fill the field music playlist with soft game music, and the boss music playlist with boss battle songs or combat music. Try to avoid stuff with lyrics of any kind if you can.
While working on mundane tasks have the field music playlist going softly. Again, video game music especially is designed to be flowy and keep you engaged without being intrusive. When you have a deadline? Put on that boss music.
I actually did this once I read that particular bit of advice with music from my favorite games and more added over time as I found more games and thus more music. It works well, I have something as sort of 'background noise' without needing to pay attention because it's songs I know and love and I've seen an uptick in my productivity since I started doing that.