I rather doubt it, and it seems like a lot of trouble to go through. Most riders in flat areas aren't that concerned about elevation profiles and in areas with substantial hills the anomalies you talk about tend to get hidden by the real altitude changes.

Pilots have an advantage since the place where they need the most accurate absolute altitude information is when landing - and airports have precise local barometric data to give them. Another use for altitude data is to maintain vertical separation between planes and there it's the relative altitude that's important. If a front moves through and everyone's altimeter goes up by 100' then the separation remains the same.

Note that the Garmin units do try to correct for barometric changes by slowly recalibrating based on the GPS measurement. That works fairly well as long as the weather changes are gradual (over a few hours), but can't deal with sudden storm fronts such as the one you encountered.