Floo & Fireplace Communication Into/Out of Hogwarts

[snazzzybird]

No: HPFGUIDX 81628

I originally posted this back in July, and got no responses.  But 
recently this topic has come under discussion again, and I thought 
I'd re-post it in hopes of hearing what some of the rest of you think.

I've been wondering about fireplace communications to and from 
Hogwarts, specifically with regard to the incident in OoP when Sirius 
was speaking to Harry in the Gryffindor Common Room fire. An instant 
after he left the fire, Umbridge's hand appeared, clutching at the 
space where his hair had been. Sirius was speaking from #12 Grimmauld 
Place. If Umbridge had gotten hold of his hair -- well, okay, he 
probably would have been able to get free. But what if he hadn't? If 
he had withdrawn his head from the fireplace with her hand still 
entangled in his hair, would she have been able to "trace the call" 
so to speak? Might she have popped out into the kitchen of Order of 
the Phoenix headquarters -- a location which does not exist for her, 
because she has not been told about it by the secret keeper?

If so, the Fidelius Charm might have rendered her confused, groggy; 
Sirius could then have hustled her out to the front door and launched 
her onto the street. Then as she wandered, in a confused state, 
along the streets, the charm might gradually lift, leaving her 
wondering "Where am I? How did I get here? Am I going mad?" 
Perhaps St. Mungo's would have been the next stop for the radiant 
Dolores.

Thoughts, anyone?

--snazzzybird, who is fascinated with Floo transportation and head-in-
the-fireplace communication.