"Wade Hasbrouck" wrote:
One time going from Bremerton (PWT) to Boeing Field (BFI), as I came up on
the North end of Vashon Island, a guy departing BFI had declared an
emergency. The radio was quiet and thought I would see if the Boeing
Controller would acknowledge me (hoping for a "standby") so I could enter
the Class D, and so I called "Boeing Tower, Cessna 738VJ, North Vashon, with
Sierra, to land",

You might want to re-read what the AIM has to say about this:

6-3-1. Distress and Urgency Communications
[...]
d. Distress communications have absolute priority over all other
communications, and the word MAYDAY commands radio silence on the frequency
in use.

If you know the controller is working an emergency on the frequency, just
shut up, stay out of the way, and let the guy do his job. By keying the
mike, you could be stepping on a critical radio call. Even if the
frequency appears quiet, the controller is probably busy on the landline
coordinating with other ATC facilities, airport emergency response teams,
etc.