Been away for a while (hence the lack of posts!) but it's good to be back.
It's hard to give either a yes or a no to this question, but the reason for this isn't too difficult to understand.
You see, the heart has its own conduction system that can spontaneously generate its own electrical pulses - and these pulses eventually contract the heart muscle. Thus, the heart can function independently of the central nervous system - it'll just keep pumping away merrily at somewhere around 70 beats per minute.
However, you can get much more use out of the heart if you can modulate this rate a little. For instance, when engaging in exercise, the greater metabolic demands of our (skeletal) muscles demand a higher blood flow. So in this case (and in many, many others) it would be helpful to increase the heart's rate of contraction. Similarly, there are other cases in which it would be advantageous to decrease the heart rate. This modulatory function is accomplished by means of the autonomic nervous system, which is connected to the central nervous system. For instance, a sympathetic nervous discharge would increase both the rate and the force of contraction of the heart.
So the heart can function independently of the central nervous system, but as a matter of fact it normally doesn't do so, and there are good reasons for that.