My understanding of the 'many universes' hypothesis goes like this: Every possible combination of initial conditions that is capable of long-term duration has occurred (or will occur, or is still occurring... verb tenses get a little strange out here), but their differences prevent them from communicating with each other. That is, nothing which exists in one of those universes can exist in any other. Hence, the often-used 'bubble' analogy.

If it can be determined that the fine-structure constant (which -- again, to my rudimentary understanding -- is a mathematical combination of many basic physical constants) is variable within this Universe without affecting its overall viability, that implies that the same is true for others. In each, local conditions could be identical to those in other universes, and communication -- not merely of information but matter -- is not only possible but, given the weight of numbers and fullness of time, likely.

To put it another way: The domain walls of multiverse 'bubbles' might be more like the membranes of biological cells, with pores where properly-shaped objects from either side can find a way in, or out.