../GtkComboBoxEntry is basically the same as ../GtkComboBox. It obeys the appears-as-list style property of the combobox, but will not look differently except for the popup.
As you can see in the screenshot above, ../GtkComboBoxEntry consists of a ../GtkEntry and a ../GtkButton with a ../GtkArrow inside it. The only special case that exists, is that it will remove the frame of the ../GtkEntry if the "has-frame" property is set to FALSE. Again I have no idea what this might be usefull for.
The popup works in the same ways as the one of ../GtkComboBox.
The ../GtkComboBoxEntry does not do any drawing itself. See the Geometry section.