To reproduce: 
1. Add RadDateTimePicker and set these properties: 
this.radDateTimePicker1.ReadOnly = true;
this.radDateTimePicker1.ShowCheckBox = true;
2. When run the project you will see that the checkbox is not read only. 

Workaround: 
RadCheckBoxElement checkboxelement = this.radDateTimePicker1.DateTimePickerElement.CheckBox;
checkboxelement.ReadOnly = true;