The evidence from the last fifty years or so of quantum mechanics indicates our universe is metaphorical rather than metaphysical. Westerners have a hard time wrapping their brain around the concept, but it means everything is not merely black and white, true or false, a dream or reality, but somehow both simultaneously. Reality without dreams is simply a physical impossibility because it represents a metaphysical extreme excluded by yin-yang dynamics and, for example, if you stay awake you will eventually hallucinate.
We should follow scientific method and there are no evidence supporting it. There is a famous saying "Extraordinary event needs extraordinary evidence" and I think that are provided no evidence for this. Furthermore most of dreams mechanism got explained thank to Electroencephalography and other methods. Another simple "evidence" (or better, little less than evidence) is that in determined situation we could control our dreams, this make improbable your hypothesis because it would need that we could control two physical masses using a brain which is in another universe.