If the staff receives an alert, I can guarantee that you'll have several moderators all looking into it.
Of course, we can't guarantee we'll do anything. Some reports we investigate result in no action, some result in an edit or warning, and some result in greater discipline.
I can't guarantee that moderators will respond to the reporting poster on every such instance; a lot of times, that will just make things worse. The best thing to do, if you're worried that a situation isn't being addressed, is to initiate contact by way of a PM with a moderator or administrator.
(Also, as an aside: I'm not sure that the "alert to a moderator" option is working for reported private messages, so it may be better to address inappropriate PMs by sending them along to a mod.)