If you already have a general system for client prediction, I would use it for pickups, too.
The main case where you don't need client prediction, is in large, ponderous processes. Steering a big ship, or driving a huge crane, would be cases where prediction really isn't needed.
When it comes to pickups, playing the local effects first (particles, sound effects) and then applying the gameplay effects when you're actually confirmed, may be a good middle ground. If you hear the “pickup” sound, but end up not holding the weapon because someone else was right beside you and got there first, then you're simply “hearing their pickup" :-D