I'm not aware of any feature developed by Game Freak or Nintendo to switch the music used in-game in OR/AS.
If there is indeed no such thing, then the integrity of the game software would need to be compromised to achieve what you are looking for. The process of modifying a console game in ways unintended by the original developer is generally referred to as a rom hack.
Making a rom hack or playing one is obviously illegal and is done at the peril of the user's console.
TLDR: No… or maybe if you join the dark side.