To be honest I have no idea how I would implement something like it.
I imagine that I would need to transform the values the timeline is generating according to the angle of the instance being affected, so the timeline will see no changes to it's keyframes, but there would be a little bit of new code doing some additional math to modify the steps the timeline generates as it progresses. Assuming I did everything right, it should work.
Another approach would be to transform the values held by each keyframe then just interpolate normally. If you imagine the origin of the timeline being it's starting position, rotate all the points around that center and it should work.
Both ideas sound pretty straight forward, but I get the feeling there are a million pitfalls and gotchas in both of them :P