Can studying a sacred language such as Hebrew or Arabic eventually lead you to embrace the related religion?

No. Plus, Quranic Arabic or Biblical Hebrew are not the languages spoken in today's Middle East. Studying modern Hebrew and Arabic will not make you fluent in reading the Bible or the Quran.

I don't think so.  Many years ago I studied Attic Greek (ancient Greek) and I felt no urge to offer a goat to Zeus or Possidon.

I don't see how one has to do with other. If the bible was in French then do you think learning French would somehow give people a reason to believe in God? Of course not.

http://en.wikipedia.org/wiki/Yale_University - Wikipedia Serious American students of http://en.wikipedia.org/wiki/Theology and divinity, particularly in New England, regarded http://en.wikipedia.org/wiki/Hebrew_language as a http://en.wikipedia.org/wiki/Classical_language, along with Greek and http://en.wikipedia.org/wiki/Latin, and essential for study of the http://en.wikipedia.org/wiki/Old_Testament in the original words. The Reverend http://en.wikipedia.org/wiki/Ezra_Stiles, president of the College from 1778 to 1795, brought with him his interest in the Hebrew language as a vehicle for studying ancient http://en.wikipedia.org/wiki/Bible in their original language (as was common in other schools), requiring all http://en.wikipedia.org/wiki/Freshmen to study Hebrew (in contrast to Harvard, where only upperclassmen were required to study the language) and is responsible for the Hebrew phrase אורים ותמים (http://en.wikipedia.org/wiki/Urim_and_Thummim) on the Yale seal.

That's an interesting question. I think it is difficult to separate cause and effect in this issue! As you point out, Arabic is a sacred language for Muslims. Hebrew is a sacred language for Jews. How many people who are interested in studying Arabic are totally uninterested in Islam? How many people who are interested in studying Hebrew are totally uninterested in Judaism? For that matter... How many people who are interested in studying Sanskrit are totally uninterested in Hinduism and Vedic religion? How many people who are interested in studying Avestan (ancient Persian) are totally uninterested in Zorastrianism? Personally, I found that studying Modern Hebrew in a secular academic setting in college deepened my interest in Judaism more than studying Biblical Hebrew for religious purposes as a kid. Others' experiences may differ, perhaps depending on whether a religion appeals to them more because of its modern context, or because of its ancient past.

To answer the question directly - you would not study these languages unless you were already an explorer.  The semiotics and hermeneutics of these languages, grammar and sentence construction provide insights into the meanings of these texts that cannot help but shake the very foundations of what you've been taught.  Learning these languages, and the meanings of hte ancients texts, left me at a decision point very similar to the scene in a popular movie called "The Matrix": "You take the blue pill [refuse to acccept what you've learned] -- the story ends, you wake up in your bed and believe whatever you want to believe. You take the red pill [dig deeper and harder into the texts] -- you stay in Wonderland and I show you how deep the rabbit-hole goes." It is inevitable for any person, of sufficient intellectual capability to explore those languages, to find themselves at a decision point...especially when you, yourself, uncover the sublime meanings of those ancient texts.  The cost of exiting "the matrix" is the world will never again be the way you thought it was...ever. By the 10th century, Arabic was the lingua Franca of Jews - 80% of world Jewry lived in Arabic speaking lands (Middle East, Asia, Levant, North Africa, Al-Andalus).  Sharing 60% of the root words, both languages are arguably important to any form of Jewish or Muslim study. Biblical Hebrew was very nearly a dead language in the 10th century.  If not for the work of Andalusian grammarians Judah ben David Hayyuj and Jonah ibn Janah.  Biblical Hebrew would have been completely lost.  A great deal of poetry was written, by poets Dunash ben Labrat, Solomon ibn Gabirol, Judah ha-Levi, David Hakohen the Ibn Ezra family of Merida, in Hebrew based on the work of these grammarians using Arabic metres. The Ibn Tibbon family, especially Samuel ben Judah ibn Tibbon were personally responsible for the creation of much of this form of Hebrew, which they employed in their translations of scientific materials from the Arabic.  At that time, original Jewish texts were usually written in Arabic, but as time went on.  see  http://www.amazon.com/Moreh-nevukhim-al-hairim-lileshonenu-ha-kedoshah/dp/B0081MYQS6/ref=sr_1_6?ie=UTF8&qid=1413911446&sr=8-6&keywords=ibn+tibbon Sa'adya Gaon's Kitab ul-ʾamanat wal-iÊ¿tiqadat ("Book of the Articles of Faith and Doctrines of Dogma"), was translated into Hebrew by Judah ibn Tibbon (1186) as Emunot ve-Deot (אמונות ודעות; "Beliefs and Opinions"). see http://www.amazon.com/Saadia-Gaon-Beliefs-Opinions-Judaica/dp/0300044909/ref=sr_1_1?ie=UTF8&qid=1413911402&sr=8-1&keywords=The+Book+of+Beliefs+and+Opinions

It did not happen to me. So far as I know from about 30 my classmates that I studied Hebrew together in far 2000 year, only one goes to synagogue, but they was almost all Russians and Russian people don't believe in hell. I think if it was class for USA emigrants more than half become religious Jews.  Or may be even more.

When you know the language, you see patterns and poetry in plain prose. It starts appearing rhythmic. And sounds divine! Although I was born a Muslim, learning Arabic changed a lot of things for me. It does bring you closer, for sure.

NO.  Today you have a vast knowledge base.  So studying a language will not make you accept the religion.  It is true that you will understand their philosophy as you need to go through many religious writings.