Ironically he has an empath for a counsellor, and he asks the android. Man, there are days where Picard just wasn't on the ball
As I recall, he was meeting with Data (and no one else) for other reasons, and asked him at the end of the meeting. So, less of Picard ignoring Troi and more of him asking the opinion of someone who was already there.
This scene ties in with the beginning of the episode where Data portrays King Henry V on the holodeck with the guidance of Picard. Data says that he has studied the performance of Laurence Olivier among others and Picard says that there isn't a better way to learn about the human condition than the works of William Shakespeare.