If you run harder, regardless of location, then you may or may not improve. It all depends on the quality of the workout. Hard does not necessarily mean better. Sometimes you can hurt yourself by running hard when you should be running steady. It all depends on what day of your workout and what you mean by hard. But let me answer the question as best I can.
Treadmill running is a inferior replacement for road or trail running. It's ok to use a treadmill if there is bad weather or you just can't get outside (for whatever reason), but it should never be used as a permanent replacement for the real thing.
You'll notice that when you run on a treadmill you bounce a little. The treadmill isn't as steady as the earth and the things shakes a little when you hit it (no matter how expensive it is). Every time your foot hit's, and the machine bounces, it sends ripples up your leg and you body. It's like hitting a baseball with a bat and not hitting the sweet spot; you feel it in your brain. Although on a treadmill you don't notice it that much, it can lead to problems over time. Your bones and body just weren't meant for that kind of thing. Road running present's it's own problems which are not nearly as bad as the treadmill. The best running is that on dirt, rocks, grass, and sand; those are what your body likes best.
Get a good 5k training meathod and stay away from the treadmill as much as possible. It's still a good tool, but to be used sparingly.
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