Responsive web design is just a technology that tries to determine what client requests for data (desktop or mobile client, from Windows or Android or Win Mobile or iOS platform, etc.) and return the most appropriate content. The client (browser) receives the same HTML regardless of what technology is used on the web server. As TestComplete works with the client only, no additional plug-in is required.
I would recommend a nice http://blog.falafel.com/31-days-testcomplete-mobile/ blog by Falafel, SmartBear's partner and also their 'Testing Mobile Applications In TestComplete' e-book (testing-mobile-applications-in-testComplete.pdf) that should be available on their site as well.