If he can show that he has a good football IQ in the pros, he could stick around for a while, but as a backup. Since we're not a spread-option team, and that Brian Kelly's spread offense is more of a hybrid between a spread and a pro-style offense, that could make it even more likely.
If the Detmer brothers (Ty and Koy) survived about a decade each in the NFL as backups, it's in the realm of possibility that Book could as well.