Can you be diagnosed with pcos without having all of the symptoms?

Yes. Pcos is associate with: 1. Being overweight (in most cases) 2. Irregular cycles (related to not ovulating) 3. Coarse hair growth (related in excess androgens) 4. Infertility concerns 5. Polycystic ovaries on ultrasound not all of these symptoms are always present.
PCOS. Pcos patients don't ovulate regularly. This may also cause other changes in hormone levels that may cause the lining of the uterus to get very thick, some male type hormones that cause abnormal hair growth or other abnormal patterns with your period. Some people report weight changes and other symptoms. You are more at risk for diabetes. Still, you could have pcos without having all the symptoms.
Yes! To be very technical you can be diagnosed with pcos without having any symptoms, but signs. Most experts (not all) agree that pcos is diagnosed based on 1) irregular/skipped periods, 2) ultrasound appearance, 3) elevated blood androgen levels. The reason it's called a syndrome is because not all patients have excatly the same symptoms.