hillbilly, if I understand phanntom's post, he is referring to the road itself, that was the old stage road. I gather this because Phanntom had a post, awhile back, about his efforts to randomly walk old stage-coach roads, in another state (which were now nothing but a dirt-road through a forest or whatever). Thus to answer the question, without going to the broader question of where to find old coins, in your area, the answer would be: It depends. Because first, you would need to define where the road was. While it may be true that it parallels/mirrors modern routes. New roads tended to be built on previously existing paths, afterall, in the evolution of roads. Yet they sometimes meandered. A new road might "straighten" things out a bit, so-to-speak. Leaving the previous trail that hugged easier flats, while a new road, during the age of steam-shovel construction, might be over yonder a bit more, and so forth. And sometimes, old passage through mountain passes might be completely abandoned, when the age of autos came, in favor of certain passes which were more favorable to current road-building.
So the bottom line is, even once you could research and determine the *exact* stage route Butterfield had, as you can guess, since you're talking old roads that stretched hundreds of miles, then .... duh .... go figure, that means that TODAY those paths could pass through a MYRIAD of different entities lands. Fed, state, county, city, utility, private, and so forth. It would be endless. So you'd have to refine your question and ask specifically which stretch. Then if you determined that some stretches were on public land, with no access problems, well then .... there you go.
It's going to be difficult to do causual research to define exact paths of the old Butterfield route, vs modern roads. Because most easy-reading material you'll come across will just say that the route followed such & roads (giving the modern equivalence road names). But as I've said, that's "close enough" for the casual reader, but isn't always accurate for what Phanntom was alluding to. It's quite possible that the old road was XX yards off east or west of the current paved road, or meandered about following the creek bottoms, perhaps even on the other side of a particular creek bottom than the current road, for instance. But for general purposes of the typical maps you'll see (of which the scale is practically useless) when the route had a path through a particular valley, and there is TODAY a modern road through the same valley, most people assume that the current road was the stage-coach route. And to a point, sure, that's 'close enough'. And in some points, that may be entirely accurate. But in other places, old roads meandered, jaunted off left or right, etc....
Needless to say you DON'T want to be metal detecting along-side a modern road, if you determined a stretch that was un-changed (as legal as it may be), because, quite frankly, all you'd find is modern cr*p from the decades of passing cars. You'd want to know where the stretches were that became bypassed, and faded away.