Perhaps. In theory at least. Living in an area with lots of incoming tourists: From talks I learned, some of them heavily rely heavily on e.g. hikr.org, a third party, that mentions the SAC™ scale a lot in tour descriptions. Never got told about what the Wiki says.
… which is of course fine, because it’s not referring to to OSM data!
Yes, it only ends up there. Regardless what the Wiki writes.
In the End, it wont matter much, gradings should remain within margin of error.
It’s unfortunate that the climbing page in the Wiki says that the YDS scale is to be tagged using climbing:grade:yds=*, if the YDS scale also covers walking and scrambling. But that’s from a proposal from 2008 and it has been barely used since. As a solution, instead of inventing scrambling:grade:yds=* for the scrambling values of the same scale, why not put everything into yds_scale?
foot_scale can become the main tag that we encourage everyone to use, and it is designed to be as globally applicable as possible. Paths in the Alps can additionally get sac_scale especially if one wants to make the distinction between T4-T6. Paths in the Sierra Nevada can get yds_scale etc. No need to invent more complicated names 
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My assumption is that it’s only for YDS => 5 and using the climbing tag for YDS 1-4 wouldn’t be appropriate. It’s been done here by people to indicate scrambling, but I feel like renderers are expecting climbing to be for technical climbing.
That was an option I proposed on the foot scale thread yesterday.
I don’t see any problem having yds/bmc/sac_scale exist alongside a foot_scale or even a climbing tag (as SAC overlaps into both along with YDS). If climbing:grade:* isn’t used much then that’d be a good reason to just simplify things by adding more high level scales. Renderers could then do some simple if/then logic to prioritize whatever one they wanted and then have fallbacks.