On a side note, not involving any specific diet, but overall caloric restriction can help reduce incidental cancer rates and inhibit tumor promotion. At least when it comes to mice/rats... there is some incidental data about people going through periodic fasting or starvation with reduced cancer rates too. So not sure about efficacy in treatment, but eating less in the long term does seem to reduce the likelihood of onset of cancerous conditions.

http://cancerres.aacrjournals.org/content/47/11/2759.short

http://www.nature.com/onc/journal/v30/n30/abs/onc201191a.html

http://cancerres.aacrjournals.org/content/57/21/4667.short

Reducing caloric intake also slows down the progression of cancer in mice.. while increases in Insulin-like Growth Factor I Levels apparently promotes the growth and formation of tumor regardless of body-weight and diet. Though;

Rates of apoptosis in the preneoplastic lesions were 10 times higher in DR-treated mice compared to those in IGF/DR- and ad libitum-treated mice. Administration of IGF-I to DR-treated mice also stimulated cell proliferation 6-fold in hyperplastic foci. In conclusion, DR lowered IGF-I levels, thereby favoring apoptosis over cell proliferation and ultimately slowing tumor progression. This is the first mechanistic study demonstrating that IGF-I supplementation abrogates the protective effect of DR on neoplastic progression.

So there might be a thing with sugars restriction and limiting the speed of progression of a given cancer.. though as you mentioned it may also affect the total effectiveness of a given treatment regime, or make the treatments worse for the patient than need be.