Unfortunately, every GPS or altitude measuring watch I've ever used, has always read zero.
Seriously, in maturely dissected terrain, like the Appalachians, whatever contour of elevation you happen to be on often wanders all over the map. You could be anywhere.
If you have a GPS, you don't need your elevation, you've already got a position. As for getting your altitude from a watch, I presume that is done barometrically, How far off could you be if your local weather is temporarily affected by a high or low pressure air mass?