Yes, published hours or NOTAM there will be a broadcast.
Wouldn't want to rely on a broadcast to keep you up to speed... Most ATC units will broadcast, not all, not all on time! As the PIC you need to be aware of published and NOTAM times if you put a flight plan through a red line. You also need to be aware of the 'activity' within the restricted area, some will be "flying areas" so activation time + 30mins will normally have you clear of danger, but a "firing area" where the grunts are watching the clock tick before pulling their triggers etc will not be so advisable to play with.