This question was influenced by this meme which makes a pretty dubious sounding claim.
The problem here is that "did loss of [x library or other storehouse of information] lead to loss of information" is, by itself, a premise that doesn't work. Single, catastrophic events may be dramatic to read about after the fact, but they are not the cause of losing texts or knowledge. I commend to your attention u/XenophonTheAthenian's post on that museum on the Nile Delta, which is the most frequent subject of such queries; Xenophon addresses not merely the loss of the Alexandrine institution but also how we do lose texts. u/rakony here specifically addresses the House of Wisdom.