No, corydoras can’t live without sand. In the wild, corydoras live along sandy river bottoms and have evolved to feed by sifting sand through their gills. Without sand, there will be nothing for them to sift.
To keep your corydoras happy and healthy, provide soft, natural sand at the bottom of their tank. Soft river sand, natural black sand, and coal blasting sand are ideal, but pool filter and play sand are also acceptable.
However, if you can’t provide them with sand, a bare bottom tank is preferable to gravel. Gravel substrate might injure corydoras’ fins and the sensitive barbels in their mouths.