I'm also basing this on the Smogon description. I think you missed the last sentence.
bulbapedia has:
Copycat causes the user to use the last move that the target used. A move called by Copycat in this way counts as the last move used.
Copycat will fail if the target did not make a move selection in the round before the use of Copycat, switches out during the round Copycat is used, or if the opponent's last move used was Copycat or Mirror Move. (Note that if either was used successfully, the move copied by that will be the most recent move used, and so that move will be copied by this use of Copycat.)
kinda confusing, but seems to mean, if you use copycat, you use copycat, then copycat calls overhead throw, making you have used 2 moves that turn, copycat then overhead throw, if for some reason copycat fails, then copycat cant call copycat, or there would be an infinite loop, but normally copycat is never the last moved used, because it makes another move be used as part of its effect.
would need to test it, but from that discription, i think it works.