Easy thwart: Run a document through a couple different languages in Google translate then back to English.
The writing will be understandable if not especially elegant, and my understanding is it's like a hash: after a couple hops in Google Translate it's not possible to "un-translate" it back to the original source document. e.g. English -> Spanish -> Esparanto -> English won't yield the original document if you then run the translations in the reverse order, and it wouldn't really be possible to determine which languages it was run through in the first place using only the end result document.
Of course, I'm sure the government could just get the Google Translate logs if they really wanted to . . .