Are molecules chiral if a rotation leads back to the same compound? I understand that if you rotate a molecule and it has the same configuration as its enantiomer, then it is indeed the same compound as the enantiomer (meso), and hence is achiral (despite having chirality centers).

If compound is rotated and the resulting Fisher projection has exactly the same configuration after its rotation, what does that mean in terms of chirality? (I'm not talking about enantiomers here,) It will have a different enantiomer (and hence not be meso), and will be polarizable, but the compound itself has exactly the same perspective if you rotate it. Does this hold any signifance chemically or stereochemically, or is it meaningless?

Take for example D-idaric acid (2S,3R,4R,5S)-2,3,4,5-tetrahydroxyhexanedioic acid).

In the below example of Idaric acid, the enantiomer appears to be a different compound. When the compound is rotated 180 degrees, it looks exactly the same. 



In the below example of galactaric acid, when the compound is rotated 180 degrees, it is a different image. This is despite it being meso.



Obviously, being meso has a lot of chemical significance (no polarization of light). But does a compound possessing the property of being rotated 180 degrees, and having the same image (in Fischer form) present any chemical significance compared to a compound that doesn't do this?
The property that you are describing for D-idaric acid is called C2 symmetry. This means that when you rotate a molecule (or any object) by 180 degrees, it appears identically to the original orientation. In D-idaric acid, the C2 symmetry axis is halfway along the bond between C3 and C4.

Having a C2 symmetry axis doesn't tell us if the compound is chiral or not. Achiral compounds have an (internal) plane of symmetry or a point of symmetry. D-Idaric acid does not meet either of these requirements and is a chiral molecule.

Galactaric acid does not have a C2 symmetry axis but does have a plane of symmetry. Galactaric acid is achiral. Since galactaric acid has stereocenters but is not chiral, we describe it as meso.