I am not sure about the technical side of the autopilot on a B747-400, but you mention that the aircraft would start to make S turns the closer it came to the VOR in order to track a radial, or I assume this is what you mean?
I would imagine the aircraft will be flying with reference to the route that was punched into the FMC therefore it would be navigating using the IRS, which would be backed up from the VOR/GPS. As the aircraft approached the cone of confusion it would fly perfectly straight and then automatically track outbound, once again using the IRS etc.
With respect to the tolerances of the airway, I would make the assumption that this would be the width of the airway itself i.e. 5 nm either side of the centreline. If you were to drift out of the airway ATC would no longer be able to offer you a radar control service and would therefore let you know about it. This has happened to me when cutting corners in the airway. Whilst flying to Exeter down L9 from CPT VOR, ATC offered us the option to cut of the corner rather than going all the way to BCN VOR in Wales to save time. Therefore we were outside the airway for a few minutes and our service was down graded to a RAS while flying outside controlled airspace, then upgraded once again to radar control when entering the southbound airway to Exeter.
Not sure about GPS tolerances, aren't VOR +/- 5 degrees?