Before I became Plat I had this a few times. After Plat of course the 48 hour guarantee kicks in, even so, its not much use if I need 2 rooms.

Whenever a hotel is blocked I just keep on searching. Rooms almost always appear when a guest cancels a room and I then nick those.

So to answer the question, yes they can, but you have to keep a watchful eye out.

Also worth adding that that the hotels may have used 4th July as one of their exceptions to the "no blackout" rule. And of course, even if they haven't and all redemption (standard) rooms have gone, bearing in mind the date you're looking for cancellations from those fortunate enough to have a room in Boston on this date are unlikely to give it up...