This particular cape will not show up as see through (sadly), any pixel that is "unfilled" will automatically generate as black when worn in game.

Forge and/or Optifine allow for use of capes (if you don't already have Forge, it's basically a passage for downloading mods). Then you'd have to download a capes mod (i.e MCCapes but idk how many versions it covers).

Check out some sites to get full instructions though--this is just what I happened to remember. Hopefully that helps :)

For any skin that users can make for player models and (I believe) mob textures, if there's a pixel that's completely empty from being erased it translates into a black pixel to fill the holes in game. As far as I know this applies to skins and mob skins, but maybe not block textures.
So yeah this would be ~just for the aesthetic~

Transparent pixels are different, hat layers on player models can use transparent pixels now (but not the first layers).