Join Date: Aug 2005
Location: Pittsburgh, PA
Bikes: '''96 Litespeed Catalyst, '05 Litespeed Firenze, '06 Litespeed Tuscany, '12 Surly Pacer, All are 3x8,9 or 10. It is hilly around here!
Yeah, there is no mechanical need for spacers any more than you need spacers under a quill stem. Once the stem is tight on the adapter and the adapter tightened in the steerer, nothing is going to move.
However, just for appearance you may want to stack spacers below the stem and above the headset locknut. I've done that on a bike with a threaded steerer/headset, the adapter you show and a threadless stem. it makes it look a bit more like a true threadless setup. Doesn't fool anyone who notices the headset locknut but it does look a bit better.