Short answer: Yes.
Pronunciation is undoubtedly very different today—but then the same is true for English of Chaucer’s or even Shakespeare’s time and today. (Heck, these days I’m reading Sinclair Lewis’s Babbit, and I’m having a hard time understanding the characters’ 1920s slang…).
And it undoubtedly changed within the Old Testament period, too, which stretched for over a thousand years: the early Israelites would probably have difficulty understanding a Judean in the time of Josaiah — and even more so a Judean of the Second Temple period, after they had returned from three generations in Babylon.
Within the Israelite tribes themselves there were varying accents and dialects: when Gilead’s men (Judges 12) captured a man whom they suspected of being of the Ephraim tribe, they asked him to say the word shibboleth, and when he said sibboleth (because Ephraimites were known to lisp), they knew for certain.
Generally, there were great cultural and linguistic differences between northerners and southerners (not unlike northern and southern England today) even during the briefly unified kingdom under David and Solomon.
Interestingly, modern Hebrew has more in common with the early Hebrew of the pre-kingdom or First Temple period than with that of the Second Temple (post-Babylon). When you read the narratives in Genesis, the Books of Samuel, etc., what is striking is how the people sound much like they do, today. When Achish, King of Gat, is reported to tell his men to expel David, who is pretending to be mad:
החסר משוגעים אני כי הבאתם את זה להשתגע עליי
(“Am I lacking in lunatics, that you bring me this guy to go loco on me?”)
Or when Michal, David’s first wife, despises him for dancing in front of the Ark of the Covenant as it is brought up from Kiryat Yearim to Jerusalem, and confronts him sarcastically:
מַה-נִּכְבַּד הַיּוֹם מֶלֶךְ יִשְׂרָאֵל אֲשֶׁר נִגְלָה הַיּוֹם לְעֵינֵי אַמְהוֹת עֲבָדָיו כְּהִגָּלוֹת נִגְלוֹת אַחַד הָרֵקִים:
(“How dignified was the King of Israel today, making a spectacle of himself in front of his servants’ mothers, like one of the gibbering vagrants?”)
—it might have been said today.
Generally, the same direct, emotional, caustic manner of speaking—almost Monty-Pythonesque in its theatricality (Life of Brian is a far more accurate, if unwitting, portrayal of Israelites, then and now, than any serious Western documentary)—still characterises the nation today. That, combined with the biblical expressions that permeate everyday speech and writing today, would make a biblical Israelite would feel right at home in very short order.
Notes by Autumn Light 
Then also Phoenician speakers would understand Modern Hebrew 🙂
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