Yes, the mobile edition of Minecraft that you download from the app store (like the Apple App Store for iOS or Google Play Store for Android) typically includes the option to download without music. This allows users who prefer not to have music in the game or who want to save storage space on their devices to exclude the music files during installation.
When you first install the game, you will be asked whether you would like to include the additional content such as music and textures. If you choose not to download this content, the game will work without these features.
If you decide later that you do want the music, you can usually go into the game’s settings and select an option to download the additional content, so you can enjoy the full Minecraft experience whenever you choose.