Would it be possible for someone to survive with untreated testicular cancer for 15 years?

Yes but unlikely: It's possible but very unlikely.

Depends: It depends what you mean by treatment. A diagnosis of cancer is usually not confirmed until the testis has been removed. Sometimes no treatment is a reasonable option after removal of the testis. If a lump has been present for 15 years but not removed, then it may not be cancer at all, although it is still important to have it evaluated.