Yes they do, my nephew flew them. There is no way to refit a B-1 for that mission and still remain a 'B'. Most likely in that area for training at high speed because they don't care if the one person that lives in that 1000 sq miles doesn't like the noise. There are low level Instrument routes all over W Texas which let B-1s practice low level high speed penetration exercises.
Yep.
Seen it my ownself.
At America’s first space port!