It's possible to get by as an independent with no Chinese language skills, just a phrasebook and a lot of patience. Just depends on what kind of a personality you have. Of the places I went on this trip, I would rank the most difficult to deal with speaking no Mandarin would be
--Zhangye (few to no English speakers);
--Jiayuguan (few to no English speakers, but a foreign tourist can only be in town to see the Great Wall, so people can anticipate.)
--Turpan (a few English speakers but a multitude of choices of sights, from which you need to communicate effectively to distinguish what you want)
--Xining (didn't seem to be many English speakers here)

Xi'an which is a well-trodden tourist track, has enough English speakers around, LanzhouUrumqi are similar to dealing with other 2nd tier Chinese cities, Dunhuang is doable, and Kashgar you can paradoxically find some English speaking Uighurs in the tourist industry, whereas the Chinese out there won't speak any. In the hinterlands of Xinjiang beyond the main towns, you'll need a Uighur-speaking guide, as you just won't get much insight on your own.

For those who are semi-autonomous but a little threatened by lack of language skills, it would be possible to prearrange a guide on a limited locale basis to assist with logistics and sightseeing in the places where lack of Mandarin presents more of a challenge, such as between the Lanzhou-Jiayuguan corridor. Turpan is also easy enough to arrange a meet-and-greet with a local English-speaking guide for that area. The additional costs of this shouldn't be prohibitive...and nothing compared with the cost of a formal, fully escorted tour.