The short answer is ‘yes’! The longer answer comes from 2 Timothy 3:16, “All Scripture is breathed out by God and profitable for teaching, for reproof, for correction, and for training in righteousness,that the man of God may be complete, equipped for every good work” (ESV). However, we often picture inspiration as God overriding the mind of the biblical author. If not that, then we picture the authors as dictating exact phrases uttered from an angel or God. While this may have been the case in some instances among the prophets and John the Revelator, we know that this was not the case for the majority of scripture.
Inspiration should be seen as a process rather than an event, in most cases. Even after one of the biblical authors wrote something down, that document could be changed later by the author or someone else. Look at the book of Psalms, for instance. It is a collection of different poems written over a very long period of time. Proverbs is also a compilation of wise sayings from different figures in Israel (and even broader ancient Near Eastern wisdom). We also see that the biblical authors rely on external witnesses, be they literary (e.g., Josh 10:13) or personal (perhaps Luke 1:2).
This shows that God works throughout history and guides history to create a certain outcome. We are not always able to tangibly prove God’s involvement. Nevertheless, He is involved. It takes faith to believe that the Bible is the inspired word of God, for it involved several human processes, including thinking of what to write, what to include, what to edit in or out. Yet God oversees and is involved in the whole process. We can confidently look at what was written by humans and also know that it was simultaneously “breathed out by God”.