Yes, the "Fingal's Cave" or "Hebrides" overture does succeed in meeting Mendelssohn's vision of the piece.
Explanation:
When Mendelssohn visited Fingal's Cave on the uninhabited Scottish island, he was so impressed that he immediately wrote a sketch of what is now known as the overture's opening theme. Lyrical in nature, this theme played by violins and cellos most likely depicts the echo Mendelssohn might have heard while approaching the cave by boat. The theme also expresses the motion of the waves going back and forth. There is even a theory that Mendelssohn meant to represent the only day of the year when the sun fully illuminates the cave.
The second theme of the piece, once developed, is much more turbulent. It still contains variations of the first theme, but they are developing to a more powerful and fierce, almost fanfare-like effect. The sea surrounding the cave and beating the shore is wild and dangerous, ending in almost hurricane-like fury.
The descriptive nature of this musical piece is one of the reasons it's being considered programme music - music that seeks to paint a scene in nature or an event.