I can't find anything on WebSockets on ask.f5.com so, unless an F5 employee says otherwise, assume there is no specific protocol support (yet).
I'd not heard of the protocol myself until you posted and it looks very interesting. Despite the lack of specific protocol support I don't see any reason why it wouldn't work with LTM. I'd recommend you don't apply a HTTP or WebAccelerator profile and use a FastL4 profile/Performance (Layer 4) Virtual Server. You won't be able to use compression or SSL/TLS offload but otherwise everything else should work as usual.
You may also want to consider making a Request for Enhancement with F5 support.