Flying through the DC ADIZ

I want to make a VFR run from New Jersey to Tennessee next Tuesday. It might be
advantageous for me to pass through the Washington ADIZ just south of the no-fly
zone. I believe that the procedure is to call up Baltimore approach, get a
squawk code, and get permission to enter the class B. A few questions -

Is it necessary to file a flight plan?
How likely is it that ATC will let me through? Conversely, how likely is it they
will just tell me to remain clear?

George Patterson
If a man gets into a fight 3,000 miles away from home, he *had* to have
been looking for it.