The nomenclature of the art is laminar --> boundary layer --> turbulence and flow separation
As we can see in the video, the first smoke line above does bend less towards the trailing edge, but maintains its form until past the trailing edge.
So, yes, the boundary layer will thicken, and there is drag$^2$, but this is a consequence of creating lift. Heavier turbulence eventually breaks the pressure gradient. Ideally, you want this to happen after the wing has passed.
This early NACA video$^1$ seemed to focus on ways to reduce drag for higher speed flight, and is worth watching in its entirety.
$^1$ see 1st comment by Wyatt below question
$^2$ higher aspect ratio wings eliminate some of this less productive area, resulting in a higher Lift to Drag ratio at the expense of some strength.