When I use Imakuni?'s Doduo's "Frenzied Escape" Pokemon Power, can I put it onto my bench after throwing the card?
No, you cannot; it ran away, remember??? It is out of play for the rest of the game.
Source: Evolutions FAQ (2016-11-03), TPCi Rules Team (2016-11-03)

Relevant cards

Note: All applicable cards may not be listed below.
XY12_112