In practice, do polar molecules actually align in an electric field?
These are two entirely different and unrelated phenomena, to the point that you'd better unsee that other question and my answer to it, if you can. Ions are very much not like molecules. Ions are charged; molecules are not. Molecules don't form the double layer, nor do they even know what is Debye length. The electric field (though somewhat diminished, by a factor of dielectric constant) penetrates the whole volume of liquid, so all molecules feel it the same way; none is shielded.

Yes, polar molecules get oriented in the electric field, albeit to a very tiny degree. Think of it this way: the molecule still bounces and rotates around, but it spends a little bit longer in the field-aligned orientation than in any other. To orient all molecules in a truly stiff way, like soldiers in formation, the energy of alignment has to overtake the energy of thermal motion, which requires enormous electric fields and is ultimately impossible, because a breakdown would occur way sooner than you get there.