No. From an IRL point of view, they played the Duration card only once, so the Duration card itself is enough of a reminder (unlike Throne Room, where the Throne Room is to remind you that you get 2 effects next turn).
From a strict rules perspective, non-Duration cards stay out only under 2 conditions
1) they played a Duration card an additional time (Throne Room, etc.), or
2) they played a card from somewhere else than your hand and "leave it there", with some more restrictions that are irrelevant here (Necromancer, errataed Overlord, etc.).
Imp/Conclave do not fall into either category (excluding an edge case with Way of the Mouse), so they don't stay out.