Whether you want to compensate the camera's auto exposure for the lighting conditions depends on a number of factors.

Cameras use various metering methods to determine the correct exposure. This is a considerable list, so I won't list and explain all of them, but two common methods are centre weighted and average metering.

Since light meters expect whatever scene you present them with to be middle (18%) grey, you will have to add x stops to your exposure when exposing a bright subject. This is because in the case of say, snow, your light meter thinks the scene consists of a very brightly lit middle grey subject, for which it then corrects by decreasing exposure. Unchanged, you'd end up with grey snow instead of it being crisp white.

When you're shooting on an overcast day, bright white clouds will have to be corrected for if these form a large part of your scene. Here is where your camera's metering method comes into play. It's not uncommon for (older) cameras to use a bottom centre weighted metering method. This means the camera will use the bottom of the centre of the scene to determine the exposure. This method comes in handy when you're photographing a horizontal scene with half of your picture being the sky. The white skies will leave the meter largely unaffected, since its sees the bottom centre as most important.
An average metering method which isn't weighted such as the method above will take the entire scene, and derive the exposure from the average of this scene. In this case, your bright white sky will be taken into account and exposure compensation would be something to consider.
In the end, it boils down to what you are photographing. Is your meter being fooled or not?

These problems are all caused by reflective metering. With reflective metering, light bouncing off of the subject to the camera is metered. A more accurate method would be incident metering. This does not meter the light coming off of the subject, but rather the light falling on the subject. This is far more accurate, as you're measuring the light present in the scene, and because it's unaffected by colours and other difficult reflections. I must add that you will probably be unable to use incident metering. It requires a separate light meter and a manual camera, yet you are using a point and shoot.

Tl;dr Yes, depending on what you're photographing and your camera's metering method. You would most likely be fine not compensating.