You could if you wanted to, but in LE if an asset is already loaded LE doesn't load it again, it just uses the currently loaded one.
In other engines (and in LE if you wanted to) you would create a SpriteManager class that loads all the unique sprites you need. Then you would give them some kind of unique id so you can identify each one. Then in your sprite class you would have position, location, sprite sheet id, etc. When you are ready to draw you call the sprites draw, which uses it's postion & rotation, and then queries the sprite managers texture by id to get the actual bitmap image returned. You could do a pointer, but it would be somewhat unsafe to give each sprite access to the actual bitmap data.