I do love the idea and technically it should be doable. But there are technical challenges which make it problematic in the long run. Effectively for every game you have to start 2 games, one on each server, for the mirroring to be possible. Example things that can go wrong:
You may end up with only one game up and running.
Even if you get both of them, one will always started later than the other (and you can’t really tell which is which before setting challenges), so the player that picked up the games later on would have more time than the bot on the server.
Another one about timeouts - it’s natural to play the moves at the very last moment, so with 30s per move, player would use 29s, but for the bot it might not be enough, as he has to deliver the moves across the net in both directions (4 net hops: 2 to the bot and 2 more to play the move).
Above problems are easy to abuse for anybody who has accounts on both servers leading to dual - win opportunities.