Sort of. The truss rod generally only affects the area from the 1 - 12th frets. But you might have to raise your bridge too.
The bridge ht. affects the whole fretboard - not just from the 12 - 24th fret.
Also, it's very common to have a high fret or two right at the 12th fret or in the area that the neck is attached to the guitar. If that's the case you'll have to have that area of the fretboard leveled, recrowned and polished. Usually this affects the high E string and maybe B string. In a Fender it's from the stress to the wood caused by the tightening of the four crews that hold the neck on and it's called the Fender Hump. But I see it all the time in Gibsons, Martins and Taylors, too.
I do it when I notice that it's time to - generally, with the change of the seasons or when I start turning the heat on for the winter or when moving to another climate or after switching to a different gauge of strings.
I find that I can get the lowest buzz-free action when I allow just a little relief in the neck - I don't like it to be perfectly straight. I don't measure any more - I know what I'm looking for.
But you might try holding the strings down at the nut and at the highest fret and adjusting the truss rod so that at the 5th to 7th fret you can just barely slide a Fender medium pick in there between the fret top and underside of the string on the bass side. Any more than that will make it feel like the action is to high in the middle frets and like the neck needs to be straightened some.
But I don't ever adjust my necks to be totally straight. Almost straight - but not quite.