Or more precisely, Polars. Flaps generate lift, but they also generate drag. The question is does a small deflection generate more lift than drag. No real way to know that without plotting a polar. What would be really interesting is to look at a polar of a typical GA craft vs a HP glider. Competition gliders rarely fly at best glide. They focus on things like headwind vs tailwind, strength of the thermals (fly faster if the thermals are strong so you can cover more ground in the strongest part of the day). The other thing is that gliders can fly a lot faster than best glide without paying a large penalty in sink rate, which shows up as a very flat polar.
A GA aircraft on the other hand, would have a much steeper polar, so flying faster than best glide would have a significant penalty in glide ratio vs a slick glider. Adding flaps would have a slower L/D max speed as both lift and drag are increased. That would likely steepen the polar even more. What would be really interesting is to figure out the min sink speed for a GA aircraft vs L/D max in different flap conditions. Min sink is useful in an engine out if you have a landing option nearby as it gives you more time to figure out your issue and restart your engine, assuming that is possible. Since we don't seem to have available polars, it's difficult to understand if there is an effective difference between L/Dmax and min Sink.