Absolutely no support, ever. I hate hate HATE captchas and I haven't even played LW in months due to stress but I gotta chime in here because captchas are a major pet peeve of mine. On the bright side, this might get me back to properly playing. Woo.
While a captcha might stop low-level script kiddies and stymie botting for a little while, it's a lot easier to break captchas than people seem to think. They literally just punish legit players, because programs using machine learning can solve captchas better than human players. So yeah, you might slow botting for a little while but you'll punish the legit majority way more than the cheating minority.
The captcha on FR is the reason why I haven't played coli in years, for example. A captcha breaks the Flow of mindless grinding in a way that isn't enjoyable in the slightest, plus my visual processing is garbage. Hence, personal pet peeve that gets my hackles up to a ridiculous degree.
You want to stop bots? Be proactive. The user suggesting keeping logs and having something check for prolonged periods of grinding/excessively quick inputs and having them reviewed by people has the right idea. It's a bit more work than just slapping ReCAPTCHA on it, yeah, but it's much better for the players in terms of gameplay satisfaction and accessibility.
Plus, the knowledge that there are logs that will have human eyes on them if need be will discourage the same low-level script kiddies that a captcha will, without hurting legit players in any way. (Save the whole surveillance society effect but that's a given in any game with bannable offenses)