It should not. You misunderstood the concept there. Suggestionbox sends the ajax request when it retrieves the data for suggestion. I.e. before the moment when user sees the list. You want to re-render something after user selects from the list.
So you need to add < a4j:support event="onselect" reRender="su1ed" /> as a child to suggestionbox itself.
now that you said it, sounds logic :) + for the records: I was overkilling the issue after testing many things. So, to make it run I also took out the reRender="su1ed" from the suggestionbox (at the beginning I thought that only should do the job...)