The rules only say you can play an Enhancement that will interrupt or negate, not that it has to be the first thing the card does. That's kind of implied, but would mean something like Priests Scapegoat (banish to negate) doesn't work in SI.
I think the current ruling is that SI suspends the removing ability, Boasting is played, searches, then interrupt/draw 3/play.
In theory, I agree with everyone else that it should be interrupt/draw/play, then search if appropriate.