I have no personal experience of this, but think it could be quite awkward. Nuts are a common ingredient in Chinese cooking. Do you eat Chinese food in restaurants at home? If you avoid it because of the possibility of nuts, then you must bear in mind that in China there are relatively few alternatives to the local food, especially away from the major centres. There would also be a language problem, both in terms of the labelling of packaged food, and in communicating with waiters etc. Of course, if you were to stick to big cities like Beijing and Shanghai, there would be less of a problem, as there are western-style restaurants and supermarkets selling western food.