The minor league phase will be Wednesday. Unless the rules change, the Memphis roster can be up to 38 players, all of whom are excepted from the minor league phase. That special 38-man roster has no direct connection to the season-ending Memphis roster.
The answer is “probably not”. Some years I can get it and some, I cannot. I do have a subscriber article on the home page which shows all of the Cardinals Rule 5 eligible players and on which roster I guess they would be placed.