missing-root The alarm will work. You need to make sure to set it in the owner profile, not a secondary profile. Also, if you've set a custom sound, it might default to the default sound (because it doesn't have access to the custom ringtone in BFU, but rather only a select few default ones), or it may not go off at all, someone should test that.
It is not a matter of it being a system app, but rather an app implementing direct boot. Google's clock app should implement direct boot support and work fine in BFU. Other apps may not implement direct boot support, in which case they won't.