I could be wrong, but from what I can tell, at least through v1.9.3, I do not see in code where it uses the image other than that configuration window. The forum code itself appears to just use the ID & Name.
The stored procs (yaf_category_list and yaf_category_listread) both provide CategoryImage in their return datasets but the DB class does not collect them, nor does the forum.ascx page ask for it.