Sorry for my ignorance, but isn't this more general than playing a sound. Presumably, you want to update the wallet balance from time to time anyway. Don't you have the same address pinging privacy problem no matter whether or not you play a jingle? I don't understand the connection to the audio file.
It's not the jingle, it's knowing when to play the jungle. Generally when you open your wallet, it only scans for some of the more recent addresses, and you have to trust us when we say we don't log them. In SPV wallets, they try to obfuscate which is your address by asking for different random ones along with yours, so the node doesn't know which is yours and which isn't. Also, it only scans it once when you open, or if you tell it to manually refresh (or if something in the wallet changes). Basically, the less often you ask, and the fewer addresses you ask for (or your own), the better. Doing a notification would basically require you to keep pinging nodes every few minutes for all or most of your addresses (since there's no way to know if just the most recent one, or an old one you gave out a while ago, is the one that will receive), and even if you obfuscate with lots of fake addresses, eventually yours will be fairly easy to pick out from the group.
FYI, chainalysis claims bloom filter obfuscation sucks, and they can get around it very easily.
Can Mycelium export list of HD addresses (even old ones, even future ones) for "watch-only" in some CSV-like format?
If you select your account, there's an option to "Export" the account in xPub format. That's the same as sharing a public address. Anyone with an xPub key can import it as watch-only and see all your addresses and balances, but can't spend from it.