User blog comment:Usiar/Observations and Whatnot/@comment-3067750-20101021204403/@comment-3067750-20101027001713

In addition to what Nystus said, you won't be able to attack something to trigger Sheen's buff prior to the Parrrley shot landing on its target due to attack animations and Parrrley reseting your attack timer.

Second, your Parrrley will still be able to crit, however the bonus damage from Sheen / Trinity Force / Lich Bane will not be factored in to the critical damage.
 * NonCrit = 300 Damage (Parrrley) + 150 (Trinity Force)
 * Crit = 600 damage + 150 damage