If Twonky Beam is findable as a DLNA server from a DLNA client, the client can access content provided by the server (but the server cannot "push" stuff to the client). The HDR-FOX (and presumably the HDR-2000T) has DLNA client capability, but is restricted on the stream formats it can handle - however, Twonky is known for being able to transcode on the fly into whatever format suits the client.
Nothing is for sure, these technologies can all be a bit flakey at best. Some versions of the normal Twonky server (V7) are known to cause the HDR-FOX to crash, even when not being used!