So, the real question here isn't "can my battery do it," but "can my alternator do it?" All of the normal running load of your car should be supplied by the alternator.
The battery is there to start the engine and to provide for high short term loads (e.g., the horn or maybe lights at idle).
You can think of the battery as storage for electrical power, it handles loads when the alternator is off-line (when the engine isn't running) and it also provides reserve capacity when short term electrical requirements of the car can't be met by the alternator (for example when the engine is idling).
The alternator provides power to recharge the battery after starting (or any other time when the battery has been drawn down), but it must also provide enough power to handle the normal loads of the car – otherwise just driving the car will drain the battery and eventually the battery will be drawn down to the point where it can't provide the power to start the car.