I doubt it. Just as with cycling, you need a warmup and cooldown to reach optimal performance.
If the treadmill was calibrated correctly, treadmill running should be faster than road running. See this chart for a reference of approximate equivalents.
IE. Sub-4 is olympic…. etc
As a personal reference, in my sophomore year of high school, I ran 5:07 and it got me into the slow heat at the conference meet. I never was a good miler.