It depends on what you mean by “winglets work.”
Winglets can reduce induced drag at the expense of an
increase in parasitic (friction) drag arising from more surface area exposed to
the flow. The result is a net decrease in drag if you fly with a lift
coefficient greater than about 0.5-0.6. That corresponds to high angles
of attack. In airliners, it means travelling heavily loaded
up high in thin air where the airplane is mushing along.
Since we fly our airplanes in regimes where the lift coefficient
is more like 0.2-0.3 (in thick air going comparatively fast), the reduction in induced
drag is slight while the increase in parasitic drag is more than slight, and consequently
the airplane goes slower.
If you want to fly your Lancair slowly like a glider near it’s best lift/drag
speed (about 135 knots IAS in a Lancair IV), there will be measurable performance benefit
with winglets.
As you go faster, the drag reduction benefits of winglets decline
and become negative as you approach cruise speeds.
As for appearance, ah, that is a subjective, not
quantitative, assessment.
Wingless Fred