The SQL engine part of osquery is backed by SQLite's parser, lexer, query planner, etc. MySQL would be awesome as well though, mostly because of how easy it might be to integrate the MySQL remote access protocol to do remotely authenticated queries!
Postgres would probably be even easier, since it already has the framework to do this (foreign data wrappers) and a nice API to write said wrappers in python[1] - 200 lines to use your SQL client as an email reader[2], I imagine that wrapping /proc would be considerably less :)
Turns out postgres is even easier. Took 15 minutes to go from "never used FDWs before, but how hard can it be?" to "got access to the process table as SQL" :)