It's probably a little deprecated, but might be useful if anyone still works with Richfaces 3.3... I defined 2 status components in the common facelet template. One is the main status that is used across application whenever an ajax event fires and it applies to the whole page, and one is "none" status that does nothing (and it must be wrapped in region):
<a4j:status id="main" onstart="(something)" onstop="(something else)" />
<a4j:region>
<a4j:status id="none" onstart="" onstop="" />
</a4j:region>
Whenever I don't want main status to appear, I specify "none" status as Andrey suggested, but the status component actually exists so the warning about non-existing component is avoided.
Don't forget to wrap it in a4j:region, or it won't work correctly - if you have 2 status components in the same region, I think that always the second one will be used, no matter what you put in status tag of your component which fires the request...