I think the answer is no, but I am not 100% sure.
If it was yes, then the dendrite of the nerve cell should each time receive a stimulus causing Na+ channels to open, when the contraction happen. Also, then it would mean that outside events could alter the function of hearth, which would be dangerous.
The heart has a special excitatory system and a contractile system - Sinoatrial node and Pacemaker cells, which control the action potentials in different portions of the heart. So heart and primarily myocardium i.e. cardiac muscle can depolarise without any external influence with a slow, positive increase in voltage across the cell's membrane.
Do nerve cells cause action potential in cardiac muscle?