There are many statements in the Bible about God, the Son, and the Holy Spirit that appear to be paradoxes. Deliberately so, because the finite human mind has to be stretched to even begin grasping something of what God has chosen to reveal to us.
When asking if the Son of God is both the Word, and the Light, it is helpful to consider the connection between God and Light. It is not so helpful (in my view) to ask Trinitarians what their thoughts are on the Son being both the Word and the Light, because nobody needs to be a Trinitarian to believe what the Bible says about the Son in that regard. However, the question needs to be directed to a particular group to be acceptable to the site, so this answer is designed to bring in a trinitarian aspect by showing how God relates to both Word, and Light, just as the Son does.
John 1:1-3 is clearly linked in scripture to Genesis 1:1-10. When at creation there was Darkness, God spoke Light into being, by his Word. Now, God is Light, and in him is no darkness at all (1 John 1:5). Then we learn long after creation that the Son of God "is the true Light" that shines in the person of Jesus Christ. Genesis 1 shows that Light came to be there, at that particular time of creation, to deal with Darkness.
Interestingly, God said that the Light was good (Genesis 1:4) but nowhere does God ever say that Darkness is good. And God divides Light from the Darkness.
The paradoxes going on here are such that it's helpful not to limit our thinking to one human man being one thing, or another thing; to having qualities that are merely physical. We're dealing with that which is beyond time and space, existing before any material, universal creation. The Word was with God in the beginning, and was God, and made everything that was made.
Read the Genesis chapter 1 account with the advantage of now knowing how John chapter 1 speaks of the personification of the eternal, uncreated Word of God, the same Word of God that said "Let there be light" to divide darkness. Only True Light could do that! Only the true Word of God could do that. Both Light and Word are equally necessary and involved in the matter of physical creation, and in the nature of the one God. That is what John's opening statements about the Son of God are designed to get us thinking about.
Of course, those who consider the man Jesus to only have come into existence some 2,000 years ago, and who died around 33 years after he had been born, just won't be able to make any such connections as I have suggested. It would be impossible, so I'm not even going to try explaining. You may take or leave this answer, but it will be a waste of time probing with further comments. I shall not respond for I'm not here to justify my views, but I do hope paradoxical statements will not stop anyone from thinking in another direction - towards lux eterna and logos eterna.