I have an application whose primary function works in real time, through websockets or long polling.
However, most of the site is written in a RESTful fashion, which
That's not a good idea. The standard isn't even finalized yet, support varies across browsers, etc. If you want to do this now you'll end up needing to fallback to flash or long polling, etc. In the future it probably still won't make a lot of sense, since the server has to support leaving connections open to every single user. Most web servers are designed instead to excel at quickly responding to requests and closing them as quickly as possibly. Heck even your operating system would have to be tuned to deal with a high number of simultaneous connections (each connection using up more ephemeral ports and memory). Stick to using REST for as much of the site as you can.