Mike, as of Jan 1, all of us need our ADSB-out to work anytime we fly into Class B or C areas anywhere in the US. The DC area is not unique in this regard.
However, pilots also need to establish radio contact with ATC before entering those areas. If your ADSB isn't working properly, ATC will almost certainly let you know, just like they would have on Dec 31, 2019 if you'd tried to fly into Class B without a working transponder. (How did you ensure your transponder was functioning before flying into Class B's back then?)
If you are trying to rely on Flightradar24 or FlightAware while you are in flight, then you are also introducing the vagaries of the cell network into the equation (and whatever mechanisms FR24 and FA use to collect and publish their data), in addition to your ADSB gear. Different phones, different cellular providers, different geographical areas, and different altitudes will all yield different results in terms of cellular data availbility while airborne, but in general, it is not highly reliable and you should not count on it working. (It's actually a violation of FCC regs to have your cell phone transmitting while airborne, though folks do it all the time and I doubt anyone's ever gotten in trouble for it.)
If you've installed your ADSB-out gear and received a good performance report from the FAA, then just go fly. If for some reason you're particularly worried about it, then call ATC early in your flight and get confirmation that it's working--that's really the only reliable option you have.
But unless you have a highly problematic system, it's likely going to "just work" far more often than it doesn't, just like your radios and transponder do.