Can a real heat engine cycle be more efficient than the Carnot heat engine efficiency?

No

Explanation:

As we know that in practical engine there always present the friction between the two parts, always there present heat transfer due to finite temperature difference, it means that the real engine can not be totally reversible engine. And on the other hand Carnot heat engine is a totally reversible heat engine. So we can say that a real heat engine efficiency is always less than Carnot engine.