No. In John 1:1 there are two distinctly different uses of the word "God." The first usage is
ton theon which means The God. That's how it's used in the New Testament when referring to God the Father. The next usage is just
theos which is the word used for "god" or "a god" and it's even used when referencing the devil some times.
Knowing that, a valid and Biblically consistent translation is the one I just showed you above. The reason the Word is just "god" is because the word isn't literally Lord God Almighty. It's referring to something godly which is what God's words are. Thus, god is qualitative in regards to the word (it has the qualities of God, but something with the qualities of God isn't God) hence "...what God was the word was."
What John would have done if he wanted to call the Word "the God" is use
ton theon, but he did not do that because John not only is a monotheist, but doesn't believe there is another God called the word.
This is proofed by more of Apostle John's writings indicating he doesn't believe the "word" is God.
In 1 John 1:1,2, John directly, explicitly, and unapologetically referred to the "word (logos) of life" that was with the Father as an
it that manifested a human.
In Acts 4:24-27, Peter and John prayed together to the Lord God Almighty, Creator of heaven and earth, while in the same breath referring to Jesus as His servant.
Following sound hermeneutics, sola scriptura, and the word rightly divided, the Biblically consistent translation of John 1:1 is that the word isn't actually God. Where the word "he" is assigned to the word is just personification. Think of the people who were reading these letters and who the writer is. John was a Jewish man who was a strict monotheist, didn't deal with human gods, and served YHWH. The way John's Jewish audience would understand John 1 is poetically. That's why the "logos" in scripture is not a literally he except in John 1. What you see in most versions is just trinitarian bias and corruption of the text. (It's common sense that spoken words aren't a person.)
This is apparent from the context of John 1. Jesus wasn't the begotten Son until John 1:18. He didn't literally pre-exist except in God's foreknowledge.
Hebrews 1
5For to which of the angels did God ever say: “You are My Son;
today I have become Your Father”