To me it seems pretty clear that the card can only be played in response to a draw two or wild draw four. It is not the only card you can't play when you want to though in the other case it won't prevent you from playing your last card.

>Agent P Card - Play Agent P Card **whenever someone plays a Draw 2 or Wild Draw 4** on you and that person must draw the designated amount of cards from the discard pile. The Agent P Card is also a wild card where you choose the color that resumes play.

My reading says this card is played in response to but getting an answer from the publisher would help.