Anytime you build in Wordpress, your traffic will go up and as a result ctr will go down because the traffic is inflated due to the site appearing now on blog search engines. The new flow of traffic is not targeted while the amount of targeted traffic is about the same and so the resulting ctr is down. Also, if you are not careful in the redesign, the actual targeted traffic will go down. But if you seo'd it well then it will eventually go up again.
You also get a lot more spam traffic as spammers target WP sites trying to post comments.
In the end, if the content and seo is good then your site will start producing more click-thu's. Hope this clarifies it for you.