Really, given that some routes are based on minimum lateral tolerances from either other routes, active restricted areas or a different controllers airspace then 1 mile could make all the difference. Remember that ATC can display relevant routes in their airspace and if you haven't been cleared direct then ATC would expect to see you on the airways and on the line.
Ok so in this respect it does make a difference. But in the case of the flight crew on the forum asking about offsetting 1nm to avoid opposite traffic it will have very little effect as it is normal that aircraft are not flying on the published routes.