You can have method in your myBean which is a valueChangeListener event.
   private boolean caldisabled;  // with getter and setter
   public void checkSelectedVal(ValueChangeEvent event){
      String selectedVal=event.getNewValue().toString();
      if("NO".equalsIgnoreCase(selectedVal)){
         caldisabled=true;
      } else if("YES".equalsIgnoreCase(selectedVal)){
        caldisabled=false;
      }
}
And in your view in primefaces calendar component set disabled attribute
<h:selectOneRadio value="#{myBean.yesNo}" valueChangeListener="#{mybean.checkSelectedVal}">
    <f:selectItem itemValue="yes" itemLabel="YES" />
    <f:selectItem itemValue="no" itemLabel="NO" />
    <f:ajax event="click" execute="@this" render="mycal"/>
</h:selectOneRadio>
<p:calendar id="mycal" value="#{myBean.date}" disabled="#{myBean.caldisabled}"/>
And there should be another way to do this. I think as this calendar component is Jquery datepicker you should be able to do it using scripting alone with no need to go to bean and make ajax call