No, it won't get its effect, it's just like the monarchs.
I have play tested trade-ins and they're seriously pointless. Most of the time I have to fear not being able to draw Barbaros/Bloo-D. If I drop them with Trade-in, it defeats the purpose of speed in the deck. So D-Draw is a better choice for I can drop things I don't want.
A second Pot of Avarice sounds viable, but I'm not too sure. Seems like too big a dead draw if I can't dump as fast as DAD Synchro decks.