With this implementation, it would not throw a stackoverflow exception but there could be an unusual behavior. Maybe there could be some better exception message to handle this case.
OverflowQueue q = new OverflowQueue(n);
 Now, let's say I want to enqueue n+1 number of elements and then dequeue the same number of elements. Here it doesn't throw any error to enqueue n+1 elements. However deQueue method will throw NullPointerException as soon as the method is executed (n+1)th times.
I would prefer to "resize the array" to avoid Stack overflow exception. There is a possibility of unused space in memory in case of resize array implementation if enqueue and dequeue are executed randomly. This can be handled by sinking the array if required.