Does putting shoe laces in the washing machine really get them back to their original color?

i've never put my shoelaces in the washing machine fearing they would get messed up and change to a different color. But i have some really bright white laces and just got a little dark stain on them, it wont come out with the usual stuff i use. So if i throw them in the waashing machine with my other white clothing would the stain disappear and go back to bright white? I have that clorox bleach pen, should i apply that on both laces before putting them in the machine? Or just where the stain is?