There's a policy regarding US routes that any new additions to the system must meet AASHTO design standards, which I take to be the same as Interstate standards. Would this apply to renovating an already existing section of a US route? Say they wanted to straighten and/or widen an older section, or even just repave a small stretch. Would they not be allowed to do so without completely rebuilding that particular alignment to the meet the current design standards?
No, AASHTO design standards are the Green Book. There are provisions for every level of highway. It has to have proper lane widths, superelevation and banking, vertical and horizontal curves, sight distance and clear zone, etc.
Interesting. Do you have a link to this "Green Book?"
http://www.worldcat.org/title/policy-on-geometric-design-of-highways-and-streets-2004/oclc/57351603
As for the original question, a renovation does not need approval by AASHTO. I don't believe a minor relocation does either, only one that changes the cities used as control points, although some states will submit all relocations. For example, none of the recent realignments of US 84 in eastern Mississippi, such as around Waynesboro (http://www.openstreetmap.org/?lat=31.6929&lon=-88.637&zoom=14&layers=M), seem to have been submitted to AASHTO (though I may be missing it due to their horribly inconsistent file naming).
I think you're supposed to submit to AASHTO every time the road is moved to a new designation (i.e. a new facility or onto a different route or road). A minor realignment or relocation probably doesn't need to go through them, though it would need to meet their design standards or have design waivers if it's in any part Federally funded.