Your pouch has nothing to do with breast feeding your baby and their stool color, except for the fact you may want to hydrate yourself more tan the average person, especially when baby is tiny and exclusively nursing.
If it's not green constantly, I probably wouldn't worry if all else is well, but I would talk to the pediatrician or a lactation specialist. They say green stools can equal too much foremilk and not enough hindmilk, so maybe that's related to your oversupply issues with baby taking in too much watery foremilk and not enough fatty hindmilk at time (getting a big rush of watery stuff at the start and filling up too fast before the more nutritious hindmilk).
And FWIW, I exclusively breast fed my daughter. She nursed for 16 months, never gave her an ounce of formula, because of the fact I'd read you could help decrease the chance of IBD by doing that (and other autoimmune issues). My sister gave her kid formula. Mine? Has had Kawasaki's Disease, and did get indeterminate/Crohn's colitis with arthritis, anyway. My sister's kid is healthy as a horse. Didn't work in my case to prevent it.