<apex:page controller="testPageController">
    <c:testComponent/>
</apex:page>

<apex:component controller="testComponentController">
    <apex:form rendered="true">
        <apex:actionFunction action="{!init}" name="init"/>
    </apex:form>
    <script>
    init();
    </script>
</apex:component>

public class testComponentController {
    public void init() {
        update [SELECT Id FROM Contact LIMIT 1];
    }
}