The short answer is yes to a large degree, but not certainly for the entire Bible. The Pictographic Proto-Siniatic script or a variant thereof was likely to be used to write the Torah, being the first 5 books of Moses. It is more certain that the rest of the books of the Old Testament were written mostly in Paleo Hebrew, being the script most Israelites are most familiar with contemporarily.
The Early alphabet, typically referred to as the Proto-Siniatic or Proto-Semitic, is the pictographic script you may have seen before which looks like little cave dweller pictures of several things like ox heads. We know that this alphabet existed in 2,000 BC and it is clear in inscriptions such as the Wadi El-Hhol inscriptions and those found in Serabit El-Khadim in the Sinai Peninsula. As I mentioned, it is called a pictographic alphabet because each letter is a picture of something. For example, the word ahlap means "ox" and the original Pictographic Hebrew letter ahlap is a picture of an ox. Alike, iyan, which means "eye" is indeed a picture of an eye.
At around 1000 BC the Proto-Siniatic alphabet was transformed into the Middle Hebrew Script, which is usually called Paleo-Hebrew the script that we are most familiar with as Israelites. These letters are still pictographic to a certain degree, though written in a simpler form. For example, the Paleo-Hebrew character ahlap is a simpler form of the Proto-Siniatic letter, but it still looks a little bit like the head of an ox. This Paleo-Hebrew alphabet was used by many people, Semitic and non-Semitic peoples in the Near East including the Hebrews, Phoenicians, Arameans, Moabites, Amorites, etc.
When the Israelites were taken into Babylonian captivity around 400 BC, they adopted the Aramaic script of that land. The Aramaic script is a continued form of the Paleo-Hebrew and this is the alphabet that was predominately written with the Aramaic, or "Late" Hebrew. While the Hebrews used this late Hebrew script, they still continued to use the Paleo-Hebrew script well into the 1st Century AD which can be seen in some of the Dead Sea Scrolls and coins minted at this time.
Modern Hebrew is very similar to Late Hebrew and anyone who can read Modern Hebrew can at least identify the characters of Late Hebrew quite easily since there isn't much difference between the two visually, apart from the vowel systems.
Whether or not Torah was written in pictographic Proto-Sinaiatic Hebrew would depend on when the Torah can be accessed to be written to determine which period of the alphabet was used. Biblical scholars largely accept that the Torah, the first five books of the Bible, was written around 1200 BC, which means that it would have most likely been written with either the Early or Middle alphabet or even potentially a form that is similar to both or even somewhere between the transition of one to the other. The later books of the Bible would have definitely been written in the middle, Paleo Hebrew.