That's what I do. You hear different things. People say that after a number of generations, sourdough cultures kept in the same environment will eventually be the same, but I don't buy it. The ones I start with bread yeast never get properly sour. Using bottle dregs worked out really well, I suspect because the yeast had to compete from the get-go with bacteria. Starting with no yeast, just gathering wild critters from the flour and the air is kind of hit or miss for me.
I'd love to see some actual analysis done, though. Everyone has a theory, but nobody bothers to prove it.