Couple of things:
Yes, Shadow Politics allows you to make a challenge outside of the Challenge phase. As doulos2k says, the reason is because you get to start that challenge as a player action. You don't need a "declare challenge" framework step, so the "additional" can be added on to "nil" as well as to "X challenges per phase."
As for the original setup of using Dany to steal all of your opponent's gold in the Marshalling phase, Khudzlin is correct that it is mechanically possible. However, if your opponent is paying attention, it'll never work in a practical sense. That's because in between you declaring attackers and me declaring defenders, and between me declaring defenders and resolving the challenges for that Shadow Politics intrigue challenge, all players are allowed to take PLAYER ACTIONS. It is still the Marshalling phase and I am still the active player, so in those places for player actions, I can take all the marshaling actions I want, including playing cards from my hand. So I'm going to spend all the gold I want, either before declaring defenders or resolving the challenge, BEFORE Dany ever has the chance to steal all my gold.
So yeah, it is possible mechanically for Player A, but it is also completely avoidable mechanically for Player B.