How essential it is totally depends. There's no guitar on Miles Davis "Kind of Blue" from 1959 which might be the most famous jazz record in music history. On the other hand, it's a fairly essential part of the arsenal of the big 70s fusion bands (just an example).
So discussing guitar's role in jazz seems a bit futile. What kind of jazz? Are you talking big band, gypsy jazz, fusion, swing jazz, modal or what?
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