Can glasses or corrective lenses improve someones depth perception?

Depth perception is created by the spacing of your eyes and their overlapping fields of view. If the objects are in clear focus maneuvering around or through them will always be better than when the objects are blurry. The same goes for close up work. In a sense it does not improve depth perception, clear vision allows depth perception to perform at peak potential.

Yes, glasses that correct vision will help depth perception.