Can brute force answer from the server quicky: http://en.lichess.org/captcha/0nbdeigw?solution=a1+a2 returns either 1 or 0. The total complexity of this to brute force is 768 possible moves. Most of us here could write a bot to spam their site with less than 30 minutes of time and effort.
Blocking bruteforce is 'easy', just make any attempts after X attempts be void for the given board/ip For the humans, just give another board (and add a time delay)
But, basically you're right. If the bot is not using an external chess engine, it could effectively be blocked from brute force attacks the way you describe.