Well, yes - if one implemented an action / extension to the general search functionality which would dynamically transform the executed search query into a smart folder with the same query, it would be possible to share the query (not necessarily the exact same results, as their permissions may evaluate differently for other users).
At a customer of mine, I once (~2013/14) implemented an enhanced search UI for Share (way before facets or smart folders were supported in the standard product), and that UI also included a "Saved Search" capability which would store the current query as well as any selected facets etc. into a node (as JSON content), and provide the ability to share that node e.g. via a shared folder in a site or the user's home directory.
Using the out-of-the-box product, you are still left to implement such a functionality yourself. I am also not aware of any ready-to-use (open source) addon which would provide such capabilities in Share, and since ADF / ACA / ADW really aren't supportive of plug'n'play extensions, I doubt there is something for them either.