I'd expect them to. The major weight disadvantage that quill stems have is the expander and redundant tubing in the steering tube area. Quill stems manage to make a little of that weight disadvantage back by not having a connector at the top of the steering column.
From a structural point of view, adapters are the worst of both worlds: you still have to have the wedge expander and a bunch of tubing overlap within the steerer, and you need to have the connection between stem and adapter up above the headset.

I suppose it's theoretically possible that advancements in manufacturing could allow the sum to weigh less than available classic-style quill stems; but in terms of the basic configuration choices, the adapter setup should be heavier than classic quill.

But, I also don't have data for comparison.