No. You will not be able to insert a conversion button or a Call To Action (CTA) button in an email campaign. One of the reason is that email campaigns do not support forms, and so there’s no scope for a CTA button.
But as a work around, you can insert an image of a CTA button in your email campaign, and link it to a landing page or a form, in order to capture lead information. For more information, see HTML Editor of the email campaign composer.