Hello, can someone explain something about texture baking, please?

If I'd paint hair in an external program (i.e. Corel Photo Paint) as a PNG or JPEG, and then apply the hair texture + transparency and bump mapping and reflection mapping to an object (i.e a plane), if I bake the texture to the object, will I still need the external texture file or could I get rid of the file and the hair would still be the same on the object?
Could I then export the object to someone else (just the maya file) while keeping the baked texture of the hair? (the person would not have the same maya project folder though, they'd only get the file).