Making sourdough Grandma's way

Yes, you can use your starter and then add water from cooking potatoes when you feed your starter. Just make sure to use unsalted potato water. If you salt water when cooking potatoes, then take a piece of boiled potato, mash it, blending it with clean water, and use it to feed your starter along with the usual flour.

Potato and potato water stimulate yeast, both are traditionally used in homemade yeast, starters, breads and rolls, so your starter will be more powerful and bread and rolls more tender, moist, and light.

This is what America's Test Kitchen says about potato effects:

Here are four good reasons why we crammed a full packed cup of mashed potatoes into our rolls.

Quicker Rise: The potassium in potatoes has a positive effect on yeast, causing it to rise faster and more vigorously than it would in wheat-only breads, which also leads to lighter texture.

Super-Soft Crumb: When boiled, potato starch molecules swell and interfere with the ability of flour proteins to form gluten, ensuring tender bread.

Moist Texture: Potato starch granules are about five times larger than wheat starch granules and are therefore capable of absorbing at least five times more water, resulting in a moister crumb.

Longer Shelf Life: Potato starch molecules hinder wheat starches from staling, thereby keeping the bread’s crumb soft for days.

Quite a few of the old bakers used to tell how they maintained their yeast / ferment  using potato peelings.