How to add captcha to pdf version
First you should avoid captcha, their are not user friendly. But good new, in this case you don't need it :).

Print module generate the pdf once and cache it https://drupal.org/node/516466#comment-6390678. So DOS are not possible on pdf generation.

You can still have DOS by requesting a pdf thousand of time, saturating your bandwidth. If you are really worried about that you can for example configure Apache with mod_evasive http://systembash.com/content/how-to-stop-an-apache-ddos-attack-with-mod_evasive/

By robot I suppose you mean search engine robot. You can add that in your robot.txt (But I think is not necessary):

User Agent: *
Disallow: /*.pdf$