Yes, leaving unpeeled potatoes on a baking sheet with a small amount of water overnight in the cooler can potentially affect how they bake. Potatoes are porous, and they can absorb moisture. If there is water on the baking sheet and the potatoes are in direct contact with it for an extended period, they may absorb some of the water.

Excess moisture in potatoes can impact their texture when baked. It may result in a less crispy or more soggy texture on the exterior, depending on the cooking method. To avoid this, it's generally a good idea to pat the potatoes dry before baking or roasting them. This helps ensure that they achieve the desired texture during the cooking process.

If you find that the potatoes have absorbed some water, you can try to pat them dry with a clean cloth or paper towel before baking. Additionally, adjusting the cooking time and temperature may help compensate for any extra moisture absorbed. Keep an eye on the potatoes as they bake and make adjustments as needed based on their texture and doneness.