It seems like you would be able to Imp it before having to play the psi game.
Imp says you can trash a card that you access, Future Perfect says when you access it, play the game. I know the runner can use paid abilities first then the corp has a go.
Regardless you still have to Psi Game it in the archives.
100% no. The psi game on future perfect is a when accessed ability. These must resolve before any other abilities can be triggered.
Page 9, Column 2, Question 7, FAQ 1.4 wrote:
Can the runner trash an accessed card with Demolition Run before any "when accessed" conditional abilities resolve?
No. The card must be accessed before Imp, Demolition Run, or any other similar effect can be used to trash it, just as if the runner was paying its trash cost.