Can I have no symptoms but still be diagnosed with gastrointestinal fistula?

Fistula. Absolutely. Fistula between to relatively close loops of bowel may result in no symptoms at all. It depends on where the fistula is and what structures are being connected by the fistula.
Yes. Fistulas are abnormal communications between different areas of the body. Sometimes these are small and essentially asymptomatic. In such cases, it can be safe to just treat these with regular observation, but sometimes the asymptomatic fistula can enlarge and become symptomatic over time.