I realized I didn't touch on this question. The answer is a qualified "sort of."
Accepting the premise that Satan walks among us, one should ask "why?"
Satan walks among us always tempting us. God created us with the ability to choose to follow Him.
Satan always works to affect that choice. Daily.
I found this part of the movie particularly illustrative of that belief. (again, you really should see the movie, as Satan walks among the crowd but the crowd is oblivious to his presence.)Satan was tempting Christ right up to the end; he was tempting Him to come down from the cross; he tempted Him to walk away from the scourging; he tempted him to put down the cross. At one point Satan is pictured holding a baby with an adult head. (It was the most disturbing part of the movie to me - the violence I could understand and deal with...the kid was just butt ugly and evil.)
My wife asked about that and after thinking about it, that brief glimpse occurs about the time Jesus appears to be questioning God's plan to crucify Him. I took that to be illustrative of a "what if." What if Jesus would have succumbed to temptation and walked away from God's plan. Would he them have become the son of satan? Seems plausible to me.
It would be interesting to buy Gibson a beer and ask him about it.