Yes, in a way. I can get the position of the constrained objects and then compute their relative positions from the constraint. However, it would be nicer if I could get this directly from the constraint. This can be done for the angular ones with the above mentioned methods.
Edit. So, a combination of what you asked to be clarified: The positon of the constrained object relative to the linear limits of the constraint. (e.g. if the object is allowed to move between -1 and 1, then I would like to know the current position between these two limits)