Yes, the Chrome Alum and Alum hardeners act by forming an ionic bond with gelatin. The Aluminum based Alum can be reversed and the film or paper can become softer, but I am not sure about Chrome Alum due to its strength. In addition, Chrome Alum forms a bond with glass plates.
Formaldehyde forms a covalent bond with gelatin and once formed it is very difficult to reverse! So the bonds are totally different in nature and in effect. As you go from formalin to glyoxal to succinaldehyde to glutaraldehyde, you also form a "longer" bond length which changes the characteristic of the hardening.