Why it might be a problem?
What do you mean?
Any samples Sergey?
Are you sure this sample deals with ajax requests?
As best I know, the FacesTraces is not about ajax or non-ajax. It just shows the result of passing the JSF lifecycle. If you re-render it during Ajax request/response, it should show the result of passing the JSF lifecycle during this Ajax request/response.
Did you even try it?
If yes, do you have any problem?
if not, why you expect somebody else to check it for you?