He needs to start CoC as soon as possible because he's going to be thinking about how "apostate" it is in the meantime. Tomorrow's Watchtower study is specifically to get people in the Borg to NOT read that kind of stuff and to NOT listen to their enlightened brother stillstuckcruz.
If there is any way you can get him to skip tomorrow's meeting and do something fun with you, that would be great.
And again, a promise to read the book isn't the same as having read the book. Until he does, he's still a possible rat.