Yes. Adobe Campaign supports responsive design content in emails.
Responsive email design ensures that an email renders optimally for the device on which it is opened.
No specific requirement necessary for Adobe Campaign. You just have to use XHTML or a responsive content format. Campaign does not transform your content and you can use any responsive content provided by your Content designer.
Because Adobe Campaign embeds an Internet Explorer type rendering for eMail preview, you may get a rendering that is different between this preview and the one you get in your final browser (if it is different from the Adobe Campaign embedded IE version or browser (FireFox, Chrome, Outlook 2013, etc...)).
Note: Adobe Campaign Digital Content Editor (DCE) module includes some Responsive design formatted templates. They are available in the Resources > Templates > Content models folder.