This paper investigates the usefulness of reasoning about the uncertain presence of obstacles during path planning, which typically stems from the usage of probabilistic occupancy grid maps for representing the environment when mapping via a noisy sensor like a stereo camera. The traditional planning paradigm prescribes using a hard threshold on the occupancy probability to declare that a cell is an obstacle, and to plan a single path accordingly while treating unknown space as free. We compare this approach against a new uncertainty-aware planner, which plans two different path hypotheses and then merges their initial trajectory segments into a single one ending in a "next-best view" pose. After this informative view is taken, the planner commits to one of the hypotheses, or to a completely new one if a collision is imminent. Simulations were conducted comparing the proposed and traditional planner. Results show the existence of planning scenarios -- like when the environment contains a dead-end, or when the goal is placed close to an obstacle -- in which reasoning about uncertainty can significantly decrease the robot's traveled distance and increase the chances of reaching the goal. The new planner was also validated on a real Clearpath Jackal robot equipped with a ZED 2 stereo camera.