Here's what a bleach pen did on 2 pieces of commerecially dyed black fabric.
Here the bleach pen has been applied to a fat quarter of my overdyed fabric. Note that although I overdyed with double strength black dye, the fabric has not come out black as such.
And here is the lattice piece when dry, along with another fat quarter. While you can see that there are other colours in the background, the discharged areas are predominantly red, orange and pale yellow shades. No blues, greens or purples, even those those colours were present. Hmmm. An interesting exercise, but it's not something I plan to do much of. Regrettably, there is not much bleach in a bleach pen, so this is not a very economical way to discharge colour either.