Most wide angle lenses will arc the focal plane to a certain degree, but the amount is dependent on it's design. There are some specified "flat field" lenses, but I don't know of any in particular. The only situation that might be of concern with a curved focal plane is when photographing a flat plane on the perpendicular. In that case, the center of the frame is closest to the lens (remember, we're perpendicular), and the rest of the subject gets further away the closer it gets to the edge of the frame. If a particular lens has a high degree of curvature in the focal plane, the extreme edges may get a bit soft as the focal plane will bend towards the lens, but the subject is further away at the far edges. They go in opposite directions. Usually, stopping down a stop, or two, is all it takes. Gawd bless DOF.
As for tilt-shift lens, you are correct. All you're doing is laying (standing?) that imperfect focal plane along the plane of your trees.
This is different than curvature of field, btw.