Can Bringer of Dreams and Nightmares' Powers benefit from Badlands?

Can Bringer of Dreams and Nightmares' Powers benefit from Badlands?

Yes.
This isn't necessarily obvious: To Dream a Thousand Deaths affects the instructions of Bringer's powers (see FAQ), and unlike most damage modifiers, Badlands applies when the results of an action deal Damage (otherwise "Badlands don't apply if Damage is reduced to 0" makes no sense). So on first blush, Badlands shouldn't apply.
However, the effects of To Dream a Thousand Deaths key off "what pieces would this Damage/Destroy instruction have destroyed if this Power were doing Damage/Destruction normally?" – and the answer to that depends on Badlands.