Is there a relationship between white fungus on the tongue and cancer?

Yes. We all have "fungus"in our mouths and tongue but when the oral cavity is healthy it is kept under control. Most cancer treatments of the mouth and throat can change this healthy environment which in turn allows the growth of "fungus" in our mouths, tongue and throat.
Possibly. White fungus in your mouth indicates something is going on, but it doesnt have to be cancer. Most often a number of other diseases can cause this such as an autoimmune disease, hiv. Thrush or a yeast infection in your mouth is also possible and very common if you wear any type of oral appliance (denture, etc). Other things that can cause it is diabetes, antibiotics, dry mouth, and pregnancy.