Raising or lowering the string height doesn't increase the open-note
string tension. If it did, it would increase your pitch as well.
Higher action will, however, increase the "feel" of tension, because you have to push the strings down further (thus stretching them more) in order to fret notes. Because of this extra stretching, it will also throw off your intonation, because the difference between the fretted note and the pure harmonic will be much greater than on a guitar with low action.