The views that the customers see are all using a viewset. Custom viewsets allow you to integrate anything that you want, both server-side and client-side. So yes, it's absolutely possible to add any kind of user interface element that you want, including CAPTCHA controls.
If the CAPTCHA control you choose to use works client-side, then this would be incredibly easy to do. Simply copy and paste their code snippets to the desired place in your viewset.
If it works server-side, then you will have a bit more work to do, probably using the action delegate pipeline integration extension point to validate the input.