Can miniature shells be seen in Earth's sand at this resolution?
Firstly I would disagree with your premise that 'most of Earth's sand contains tiny shells resembling sea shells'. Such biogenic sand is certainly true of some biologically productive sedimentary environments, but certainly far from all. For example, try finding shells in most of the sand in the Sahara desert, or any other desert for that matter. You will only succeed if the sand is reworked from previous biogenic sandstone.

As to the resolution of shells at the apparent scale of your photograph, it depends upon the biota involved. The bioclasts vary from several millimetres to true microfossils - far below any visible resolution, and maybe even below resolution of small microscopes.

I assume that any close up photo of Mars sand would have been magnified, contrast stretched, and computer image enhanced. Had there been any bioclastic grains, I am sure it would have been front page news around the world.