To increase the user experience I wanted to get rid of the captcha on the registration form. Instead I wanted to place it on the one-time login form, as not to scare off potential new members. This registration flow is also used by other websites, e.g. mailchimp.com.
I added the captcha to the 'user_pass_reset' form using the captcha administration ui and it correctly appears on that form. However when the form is submitted, the captcha answer is not evaluated, instead the user is immediately redirected to the user profile page.
As far as I can tell, the captcha response is not checked because the action of the form changes. Please correct me if I'm wrong here, I'm not that proficient with Drupal (yet).