It would yes, because it works with calcium ions. Hemophiliacs bleed because they have a mutation in clotting factors (proteins).

Chitosan and the list are really cool compounds. Glutaraldehyde as a crosslinker is a bit meh though. It will sterilize, but it’s also really not something you generally want to get on your skin, it’s pretty irritating. They’re using it because it’s very good at linking to things with primary amine groups (basically on the end of a carbon or other chain, exposing an NH2 group somewhere). Chitosan has primary amines on it. So chitosan sort of makes the scaffold with the glutaraldehyde and the alginate interacts with calcium to make a nice hydrogel. I haven’t read the paper but I’ve worked on biomimetic surfaces with chitosan and other materials before. I’ll read the paper and change this if I think it’s wrong.

Edit: Yeah more or less this is what’s happening, with gum also forming the scaffolding: