If you are resourceful, outgoing, and don't mind enduring frustrating moments on occasion, I would say "yes". Just pick up a current LP, and head to Kashgar with a positive attitude, but you might want to consider adopting a completely flexible approach (as in not planning much of anything in advance). The reason I suggest this is that you will surely encounter other travelers who either speak Chinese or have arranged guides that are doing interesting things, who may invite you to tag along with them.

It's easy to get by with English in the hostels and those cafes that are run by foreigners, and eating is pretty simple as well (i.e. there is chuan everywhere in Xinjiang).

Lastly, if you arm yourself with a few of our phone numbers before you leave (most of us speak Chinese), you'll have "concierge support" when you need it (e.g. trying to buy train tickets).

Basically, if you consider yourself to be a type B traveler, then go for it!