Depends on the animal, whitetail deer which is what those of us in the East hunt at long range will as a rule not run off unless hit or even singed by the bullet.I guess everyone has their own experiences, out here in the fall it's not unusual to see a 30*f swing. Elevation is less of a factor for me.
Yes a sighter is the best data you can have but not usually going to send a sighter with the animal standing there. you are gonna do it earlier in the day or the day before to make sure your data is holding true meaning that you can trust it later in the day or the next day.
Fact is it isnt uncommon for them to sniff the ground where a bullet impacted.
Elk are apt to behave very similar and not run after a shot.
Black bear on the other hand will as a rule run on the first shot.
Problem is there is lots of theory coming from the lips of those who have never actually hunted.
Also realize that it has been being done very successfully for decades before some of these devices were even thought of.
If you have a rutting buck situation, an uncooperative doe could take him off the hillside and gone before you ever get a shot.
And that can happen in minits.
Thats called realville, not dreamville.
But what you do can often make a big difference in the outcome.