That depends entirely on the user's preferences settings.
Typically, a mention will only alert someone when they log into the site and check alerts/followed threads. It's a polite way of getting someone's attention without the possibility of the site sending an email notification of a Private Message to them.
The problem with someone clicking on the mention link (member ID) THEN "sending a message," is that they are often only sending a profile post from the member page and those are public posts. Only "Start Conversation" is private.
