This article is from the Photographic Lenses FAQ, by David Jacobson with numerous contributions by others.
Yes, but maybe only a little bit. If the object is far enough away, the depth of field will cover the shift in distance.
An approximate formula for the minimum distance such that the error will be covered by depth of field is given by
d = w^2/(2 N c)
d = minimum distance to make the point be sharply rendered d is measured from the film plane
w = distance image point on the film is from center of the image
For the 35mm format w^2/(2 c) is 5.4 meters, so you can recompose the image with the subject at the edge of the frame and still have it be sharp if the subject distance (at the center) was at least 5.4 meters (18 feet) divided by the f-number. See the technical notes at the end for a bunch of assumptions.