Not always.
I did my 3rd FP on July 3rd 2007 and no LUDS till now.
I called FBI and they said my results sent back on 5th July 2007.
There are lot of GC's approved without LUD changes too. My assumption is it depends on the IO who is working on your case. If they have your file till yuo are done with FP, they update in the system. If they start work on different case, then they may delay.
However, you can receive RFE at any stage but that doesn't mean your Name Check completed. I am not sure how USCIS processign cases. May be periodically they start work on some group of files, and after soem time move it to different work.