Sorry to disagree with the post above, but no, your accuracy will not change.
I have tried to calibrate my Watch multiple times using different versions of Watch OS and calibration does not work. With Watch OS 2, they use an average stride length which is longer than most people. This means the Watch calculates a longer distance when used without the accuracy of the phone's GPS. I do not run on a treadmill, but it definitely does not work for Outdoor Runs.
In my case, Watch OS 2.0.1 was off by a factor of 1.25 (7 miles run is recorded at 8.75 miles) and Watch OS 2.1 is off by a factor of 1.3 (7 mile run is recorded at 9.1 miles). This was before and after "calibrating" the Watch for 120 minutes, 14 miles and over 22,000+ steps.
I hope they either fix the calibration or allow us to manually enter our running and walking stride length in a future update of Watch OS.
TxWatch
I must say first that I run the same route almost all the time and for weeks I brought my phone and calibrated over and over again. I would walk, run, jog, HIIT and the complete cycle with the phone and watch was 1.78 to 1.81 in the open woods and trails. clear sky's above me all the time. Some gills and declines and large round-abouts. Same distance. Each and every time on this phone and watch calibration. All in all, I calibrated 20+ times at various speeds on the same distance and never varied beyond 1.78 and 1.81 miles. Frankly the difference was the drifts around the corners when running fast versus walking the same turns.
Month later,'same walk or run or jug or HIIT keeps coming back with 1.75-1.8 range in 16-18 minutes. Always very very close.
I put on the watch and plug in my bests Bluetooth in-ear headphones and do an outside 5k without my phone and love having just my watch and Bluetooth earbuds that don't come out - shorts and T and Merrel no support shoes and my watch comes in with 3.05 to 3.12 each of the 5 times I have tried.
It pays to calibrate over and over when you have the time. As for the treadmill, it would take more calibration of the machine but never can be the same as the ground outside won't reduce your friction and give you a boost with each step.
If you bed super accurate with gps
Built-in and you don't mind giant devices on your wrist for $600 and then wired headphones or no headphones, go for. If you are a serious trainer the AW isn't ready.
Watch 2 with GPS will sell others but probably not me because my competing times are done. I more apps for fitness, those other sensors that Microsoft was able to add and watch faces along this line with complications around the edges. Center the watch and add complications matching color schemes that can be change.
Sell watch faces for $1-$3 and if they look good, Apple can line their pocketbooks with $30-$40 mm from all of us with no fee to developers. <end rate>
I love my SS and 7 bands.