If Apple uses chips based on TSMC's 20-nanometer process, it would have two benefits for practically all consumers:
1) Power consumption would be reduced, thus resulting in longer battery life.
2) Clock-for-clock speed increase over the current A6X chips, thus resulting in Safari being snappier.
Your assumption is correct in its simple form. But as iOS and Apps get bloated, most of the increase in processor speed is offset just to cater iOS and Apps. End user sees only tiny bit of improvement. That's why all companies just compare the processor speed in their marketing without talking about OS/App requirement.