As it seems, it is possible to perform headless tests with Selenium. The browser does not need to be displayed for the test to be run.
There is a web page which says that RFT does not support headless mode fully: http://www-01.ibm.com/support/docview.wss?uid=swg21215740
It refers to a RFE number RATLC00471121 which I cannot find anywhere else on the web. And it refers to rich clients.
I am thinking about running web clients in a headless mode. I don't know yet if that is a good idea. But I like to know if that would be possible with RFT for web application testing?