I intend to give a brief and fairly unnuanced answered to this question, by way of analogy. I have often heard the question, “Can I be saved (or alternately phrased, “Can I go heaven”) without speaking in tongues?” By this it is meant, is one able to be a true member of the family of God which participates in the resurrected life of the renewed creation, without having a devotional prayer language (often called glossolalia)? To this, the answer is “yes…but why would you want to?” In other words, why would you simply settle for “making it in?” In 1 Corinthians 14, Paul evidently perceives a great value to the personal practice of speaking in tongues and wishes all the Corinthians would do it. Thus, why not aim for everything we can have in this life? Why not set our vision higher, rather than acquiesce to the least common denominator?
Thus when someone asks me, “Can I understand the Bible without knowing Greek?,” I reply, “Yes…but why would you want to?” If you are able to learn Greek, in other words,
if you are able to learn another language (which is true of the overwhelming majority of people in the world, since outside of America it is normal for even illiterate and uneducated people to speak two, three or even four languages),
and if you have some time (which most Americans do since they spend 5 hours a day on average watching television ; it only takes 3-6 hours a week, plus or minus a few, to learn Greek in about two years)
then why would you not aim for the highest level of comprehension and understanding through the steady process of learning the languages in which the Bible itself was breathed forth by the Holy Spirit? God deemed fit in the fullness of time to send forth his Son to redeem humanity from the curse of Sin and Death. He also deemed fit that the account, exposition and implementation of this glorious redemption would be breathed by the Holy Spirit in the Greek language. The thirsting soul in pursuit of God is often led by love to learn this very language in order to know the Scriptures more profoundly, and through them, to know the God of the Scriptures with increasing clarity. Pastors, teachers, reformers, mystics and revivalists throughout history have turned to language as both an expression of love and a means to deepen love. John Wesley would spend his mornings meditating on the Greek New Testament before preaching from that very text on horseback. George Whitfield would spend two hours a night, after long days of ministry, often on his knees, doing the same. At age 24, George Muller would spend 10 hours a day studying the Bible in the original languages.
You can surely learn and understand the basic truths of the Bible without knowing Greek, but why would you want to?