Certainly in the v. low Reynolds number regime of indoor fliers, flat plates do remarkably well. There are a lot of Gottingen studies of flat plates and curved flat plates at low Re, and they seem to be pretty good at v.low Re - e.g. sub 60 000.
Am I right in saying these sections work because the more boundary layer is a more significant component at v.low Reynolds number rather than high reynolds number. Is it because the boundary layer is laminar at these Re's?
Yes, the main problem very low Re airfoils have is laminar boundary layers and the fact that this laminar boundary layer can't support large pressure gradients without separation. In layman's terms, fat airfoils don't work at low Re because the airflow can't stick to a really curved surface. An extreme example would be a ball.
Curved plates work well, but real airfoils work better. Often times, a turbulator will be used to energize the boundary layer to prevent separation at high Cl. This turbulator can be as simple as a length of thread glued to the upper surface of the wing, at about 15% chord. Attached is a pic of a couple airfoils suitable for the Re = 40k-80k range. Less camber is normally used at lower Re.
-David