The position should be fairly accurate, as it is probably taking from some of the airplane's navigation systems. Even if it isn't, the image you posted can't be expected to be accurate to more than +/-100 miles or so, due to the map scale and size of the airplane icon. But at closer zoom levels, you can see the accuracy is much better.
It's certainly possible that the system uses the pre-programmed flight route and estimates the position based on time. But especially on a long flight such as this one, conditions enroute like winds could significantly change the flight time, enough that it would be obvious that the location was wrong.
Airplanes generally will fly as direct as possible, since that would be the route that requires the least time and fuel. However, winds or significant weather may require the plane to change its path.
In the picture you posted, you can see a slight turn to the right over Newfoundland as the plane is entering the North Atlantic Track it is following for this flight.
So if the MH370 plane had this equipment, and it wasn't somehow disabled, then yes, the passengers would have seen the real location of the airplane.
See also another question regarding this display.