Answer:
No. EMTs never diagnose. We don't have the equipent nor supplies to diagnose any condition or disease. We treat for signs and symptoms that we can see. If I can test your Blood Glucose and see that it's too low, I can give you oral glucose (treatment-short term), but I can not diagnose you with hypoglycemia or the opposite, diabetes. I can't test your BG and see that it's too low or too high and say "hey dude, you're diabetic!" It's not my place or my job.
After becoming a paramedic, you can do some diagnostics (like with EKGs and other equipment) but it's still not your place to tell a paitent "you're having a heart attack". That's what protocols are for. If you see a certain rhythm, or test a BG, your protocols tell you exactly what to do for that rhythm or that measure.