That’s certainly possible. From the outcome, however—assuming it was Scripture He wrote—perhaps a better possibility might be, “I desire mercy, not sacrifice” or something similar.
Regardless, God chose not to reveal to us what Jesus wrote. Instead, all we have is the spectacle of Jesus taking time for due consideration of some type before He addressed the crowd. Indeed, who can doubt that the time he thus absorbed was designed to calm the passions of the rockholders?
So, that calm, deliberative, reasoned process remains our example.
I would normally agree with you, because that is a reasonable supposition on the verse. However, I believe none of the Pharisees and scribes cared one whit for mercy in this situation, they wanted to find Jesus in a fault. But having the possibility of themselves being stoned for their misdeeds was an outcome they were not interested in. Jesus already had shown He knew many things about people and they could have deduced He knew something about them, especially if He was writing that particular reference.