oh yes, I remember telling my mother and farther the same thing while I was studying for exams. They complained a lot, I ignored them a lot and eventually they stopped telling me, a lot.
The simple answer, is yes and no lol
Yes, it is true when it comes to memory recall. It has been proven that if you associate a concept to a song and/or the word within a song or the melody of a song it helps you recall the concept from memory much easier. This is good for subjects like history, humanities, geography, Biology, Psychology etc
No, it is not true when it comes to learning figures or facts. So subjects like maths, physics, charts, tables etc. However, converting equations into song-form has been proven to increase grades in students.
What is important to understand is that music has lots of benefits, including making you feel better and surely a happy student will do better than a less happy student without his music. You can then advise him on how to use his music to help him study better by suggesting he links some of it to his subjects or pay careful attention and see if you can make the links for him? then suggest them in that way that only a parent can do
Have a read of this link and see for yourself how music affects the Brain and how you can use it to your advantage.
Hope that helps