Doesn't look like it. There are a lot of references to the book of the Law being written down and its importance. As far as the rest of their history, perhaps they depended on oral tradition for some of it, but what made it into Scripture wasn't always written down after the fact.
And God Himself gives the reason for writing down what He said.
Deuteronomy 17:14, 18-20 14"When you come to the land that the LORD your God is giving you, and you possess it and dwell in it and then say, 'I will set a king over me, like all the nations that are around me,...
18"And when he sits on the throne of his kingdom, he shall write for himself in a book a copy of this law, approved by the Levitical priests. 19And it shall be with him, and he shall read in it all the days of his life, that he may learn to fear the LORD his God by keeping all the words of this law and these statutes, and doing them, 20that his heart may not be lifted up above his brothers, and that he may not turn aside from the commandment, either to the right hand or to the left, so that he may continue long in his kingdom, he and his children, in Israel.
Deuteronomy 28:58-59 58"If you are not careful to do all the words of this law that are written in this book, that you may fear this glorious and awesome name, the LORD your God, 59then the LORD will bring on you and your offspring extraordinary afflictions, afflictions severe and lasting, and sicknesses grievous and lasting.
Deuteronomy 29:20-21 20The LORD will not be willing to forgive him, but rather the anger of the LORD and his jealousy will smoke against that man, and the curses written in this book will settle upon him, and the LORD will blot out his name from under heaven. 21And the LORD will single him out from all the tribes of Israel for calamity, in accordance with all the curses of the covenant written in this Book of the Law.
Deuteronomy 27:1-3, 8 1Now Moses and the elders of Israel commanded the people, saying, "Keep the whole commandment that I command you today. 2And on the day you cross over the Jordan to the land that the LORD your God is giving you, you shall set up large stones and plaster them with plaster. 3 And you shall write on them all the words of this law, when you cross over to enter the land that the LORD your God is giving you, a land flowing with milk and honey, as the LORD, the God of your fathers, has promised you.
8And you shall write on the stones all the words of this law very plainly."
Deuteronomy 31:9-13 9Then Moses wrote this law and gave it to the priests, the sons of Levi, who carried the ark of the covenant of the LORD, and to all the elders of Israel. 10And Moses commanded them, "At the end of every seven years, at the set time in the year of release, at the Feast of Booths, 11when all Israel comes to appear before the LORD your God at the place that he will choose, you shall read this law before all Israel in their hearing. 12 Assemble the people, men, women, and little ones, and the sojourner within your towns, that they may hear and learn to fear the LORD your God, and be careful to do all the words of this law, 13and that their children, who have not known it, may hear and learn to fear the LORD your God, as long as you live in the land that you are going over the Jordan to possess."
2 Kings 17:35-40 35The LORD made a covenant with them and commanded them, "You shall not fear other gods or bow yourselves to them or serve them or sacrifice to them, 36but you shall fear the LORD, who brought you out of the land of Egypt with great power and with an outstretched arm. You shall bow yourselves to him, and to him you shall sacrifice. 37And the statutes and the rules and the law and the commandment that he wrote for you, you shall always be careful to do. You shall not fear other gods, 38and you shall not forget the covenant that I have made with you. You shall not fear other gods, 39but you shall fear the LORD your God, and he will deliver you out of the hand of all your enemies." 40However, they would not listen, but they did according to their former manner.
I expect that literacy in nation of Israel was more common than most of us would think.
How else does one explain a lowly shepherd boy, David, writing Psalms with the skill that he did. Or the prophet Elijah writing letters or the mention of a “book” of Adam’s history at Ge. 5:1.
One only needs to look at what the liberals teach in schools about history to understand how important it is to rely on what was written when things first happened rather than what gets told orally over the centuries. The same people who would condemn liberals for not upholding the original intent of the founders of this country think nothing of placing their eternal future on the accuracy of word of mouth story telling.
****18”And when he sits on the throne of his kingdom, he shall write for himself in a book a copy of this law, approved by the Levitical priests. 19And it shall be with him, and he shall read in it all the days of his life, that he may learn to fear the LORD his God by keeping all the words of this law and these statutes, and doing them, 20that his heart may not be lifted up above his brothers, and that he may not turn aside from the commandment, either to the right hand or to the left, so that he may continue long in his kingdom, he and his children, in Israel. ****
This is speaking about the king they have set over themselves. It is the king who is to read the law that is written so that he will be faithful to it as he leads Israel.
****11when all Israel comes to appear before the LORD your God at the place that he will choose, you shall read this law before all Israel in their hearing.****
The written word was given to the ELDERS so that THEY could read it to the people.
12 Assemble the people, men, women, and little ones, and the sojourner within your towns, that they may HEAR and LEARN to fear the LORD your God, and be careful to do all the words of this law,
The people needed only to HEAR what was written, they did not all read it for themselves. The ELDERS read it to them and thus they HEARD it and obeyed.
However, until the middle ages, the Mishna, (not the Tora) was never written down. Some things can be very accurate when passed down.