This hasn't happened to me often yet, so I could be completely wrong about the current behaviour :)
Having just started to answer questions I find that I go off to research an answer, meanwhile
Jon Skeet Tony the Pony jumps in and answers it. If I had started typing an answer I would see the alert immediately, but without typing I don't get an alert.
Also, if I were reading a question I wouldn't see the alert and may miss reading an answer.
It would be nice if the "new answer" alerts appeared regardless of what you were doing on a question page.