Official FAQ from wiki.dominionstrategy.com:
Normally, nothing will prevent you from returning Madman to the Madman pile, but you may fail to due to playing Madman twice via Procession, Throne Room (from Dominion), or King's Court (from Prosperity).
So, for example, if you Procession a Madman, you will get +2 Actions, return Madman to the Madman pile, draw a card per card in your hand, get another +2 Actions, fail to return Madman and so not draw cards the second time, fail to trash Madman, and then gain an Action card costing exactly $1 if you can.
So, the cards are conditional on returning the Madman, the actions are not. So you do play it twice.