No, we don't use accents to distinguish between words that are written the same way, but pronounced differently; the meaning and pronunciation of pesca (fishing or peach) are easily understood from the context. Actually, the fruit is pronounced pésca in many parts of Italy.
There are other homographic words that can be difficult to pronounce: capitano is a verb if pronounced càpitano (they happen), while it's a noun if pronounced capitàno (captain). Also ancora which is an adverb if pronounced ancóra (still, yet) or a noun if pronounced àncora. Another common word is principi: prìncipi is ‘princes’, while princìpi is ‘principles’.
I just read today on the newspaper a letter where the missing accent in princìpi is lamented. Actually the object is wrong: the vast majority of Italian words are accented on the penultimate syllable, so the graphic accent on princìpi would be absurd; I could understand accentuating prìncipi in case of possible ambiguity.
But in general, accents are not marked in Italian, except, curiously, when they fall on the final vowel of the word. It's a very old orthographic convention, reminding when the fall of a final syllable was marked: cittade or bontade became città and bontà. The apostrophe was later turned into an accent.
Of course there's no real reason, other than respecting history, to mark those accents now that the ‘full’ words are not used any more.