[Wm.Jacobson]

In a perfect world, yes; however, this is often not the case. For example, a high action will cause you to have to stretch the string more and will pull the fretted note sharp. If there is any relief in the neck at all, this condition gets worse as you move down the neck. Intonation is one reason not to rely entirely on the tuning of the open string. Play your chords, listen for sour notes, retune as necessary (or just settle for close enough). Whatever’s right.