You don't have to be "exact". But the closer you get the better.
If you do as you describe, you have left out the thickness of the barrel wall. You need:
Center of scope to top of barrel + Thickness of barrel wall + 1/4"
Note that if your measuring at the scope tube (which I would) and you have a tapered barrel then using the above you're going to be off since the barrel wall thickness is different at the muzzle end of the barrel and where your scope is mounted. The more the taper, the more you're off.
You're interested in the centerline of the barrel to the centerline of the scope. Lay that deer slayer on the bench. Use a dial caliper (tape measure or nice ruler if you don't have one). At the reticle adjustments, measure from the center of the scope tube to the center of the barrel. The stock on most rifles if very close to the centerline of the barrel, so eyeball it and you'll be close.
I hope that makes sense.
The proof is at the range. Get all your info and put it in the Hornady ballistics calculator. Figure out where you want the bullet to zero, how high and 100, etc. and get all you info from the calculator. See where the bullet should be at 50 yards and go shoot at 50 yards. Adjust your scope to where the bullet SHOULD theoretically be 50 yards. Now your rifle is set up to agree with what the calculator says. Then shoot at 100 yards, and your bullet should be where the calculator says it will be. If it is, then you bullet should hit at 200 yards just about where the calculator says. If the 100 yard shot is way off, then either your BC is wrong, your veloicty is wrong, or your scope height measurement is wrong and you're going to be off at 200 yards.
Ultimatley you need a 50, 100, 150, and 200 yard range to shoot at. But I don't have access to that so I do the above. Works pretty good out to 125 yards, which is my longest shot yet.
Hornady has an app for your phone if you roll that way.