Yes, Frank certainly encourages Taplow’s comment on Crocker-Harris although he pretends to do otherwise. First, knowing well the rules, he asks Taplow why Harris-Crocker has not told him his result yet. However, when Taplow tells him that Crocker-Harris is ‘like that’, he snubs him. So, Frank is all the time trying to be very clever. While asking Taplow to be quite, he does everything to encourage him to comment on Crocker-Harris.
When Taplow imitates Crocker-Harris, Frank tells him that he has gone too far but just after that he asks Taplow to repeat the imitation. Obviously, he enjoys when he thinks Crocker-Harris is being ridiculed. Again, when Taplow refuses to go back home, Frank asks him if Harris beats him and the other boys. In the end he asks Taplow ‘not to be so selfish as to keep a good joke’ to himself.
Thus, Frank encourages Taplow to comment on Crocker-Harris again and again while pretending to do otherwise.