Yes, but in a very different way. QM alone pushes more to parallel universes that do not interact at all.
But we really cannot know that, and quantum physicists and cosmologists sorta warned us about getting too carried away with the parallel universe stuff.
As far as interaction is concerned, that may well depend on which stage we may be talking about. With brane theory, for example, these waves may spin off a "universe" from their interaction, but once spun off and going in different directions the degree of interaction after that may be close to nil.
The main thing qm does is to indicate the unpredictability of sub-atomic particles, including that there may be even parts of our own universe that may behave under different laws of physics.
No matter how we may try to look at this, much is likely to be even beyond even our imaginations since our brains are more patterned with how we perceive mega-matter versus sub-atomic particles, the latter of which we know so little about.
Interesting discussion though.