You can check the value of the switch in the renderedparent attribute of the output text. You can use the <f:ajax>switch group inside to update the parent text of the output each time the switch is changed.
Kickoff example:
<h:form id="form">
<h:selectOneRadio value="#{bean.radio}">
<f:selectItem itemValue="one" itemLabel="This should hide output text" />
<f:selectItem itemValue="two" itemLabel="This should show output text" />
<f:ajax render="output" />
</h:selectOneRadio>
<h:panelGroup id="output">
<h:outputText value="output text" rendered="#{bean.radio == 'two'}" />
</h:panelGroup>
</h:form>
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<h:form id="form">
<h:selectOneRadio value="#{bean.radio}" onclick="document.getElementById('form:output').style.display = (value == 'two' ? 'block' : 'none')">
<f:selectItem itemValue="one" itemLabel="This should hide output text" />
<f:selectItem itemValue="two" itemLabel="This should show output text" />
</h:selectOneRadio>
<h:outputText id="output" value="output text" style="display: #{bean.radio == 'two' ? 'block' : 'none'}" />
</h:form>