If the move calls randomly from a list of moves like Assist and Metronome do, then definitely not. Move substitutions rely on knowing what your opponent will do before the first action begins and you cannot know beforehand what move is going to be called. Even if all the possible moves fit the substitution's criteria (for example, an Assist that calls Earthquake, Earth Power or Mud Bomb fitting the criteria for damaging Ground-type move), technically he didn't order the move that's being called.
For ones like Copycat and Mirror Move, there is a risk of causing an infinite loop. Like, say your first action is Surf, and you sub for "if damaging water-type move then change that action to Dig" and your opponent uses Mirror Move on action 1 to copy your Surf. Suddenly, your action 1 would change to Dig, which would mean his Mirror Move would call Dig, so your sub wouldn't activate so you'd use Surf, which means the Mirror Move would call Surf, so your sub does activate and ...
Yeah, I think moves that call other moves do not activate move subs based on the properties of the called move. Using Sleep Talk or Copycat only activates move subs for Sleep Talk or Copycat.
Using Assist to call Mud-Slap could, however, trigger a chance substitution for "if your accuracy stage is below X by action Y" or "if your HP is below P on your turn on action Q".