I'm not sure the Mycelium app updates the balance automatically. I often have to hit the refresh icon to see changes, but that could be because my Internet connection has a high latency, idk.
I think that due to security reasons, external application (different from Mycelium) should be used for address watching and making beeps. Do not know if such application exists, but it should not be difficult to make.
Can Mycelium export list of HD addresses (even old ones, even future ones) for "watch-only" in some CSV-like format?
The post by Rassah just above (quoted below for convenience) suggests a privacy issue, not a security one. I thought SPV clients already had a way to request some superset of transactions they're actually interested in to protect privacy (though clearly not as well as a full node requesting every transaction).