It would be a huge, probably unmanagable task. Somehow like the race betweeen Achilles and the tortoise. By the time someone would have translated the whole bunch of messages up to a certain date a new bunch of messages would have arrived.
Ok, the standards for translation would not have to be as high as the standards for translating books; the translator would not have to rack his or her brain just to find a similar expression for the translation of an idiomatic phrase, it would be enough to convey the meaning. Nevertheless, even though a rough translation can be written just like this by a trained translator, without much thinking required, the sheer amount of messages certainly would eat into the translator's spare time.
Why do I expound on this? Because I would be an obvious candidate for German/English translations and vice versa; I used to translate on a professional basis for over 4 years.