It will increase memory footprint due to the extra buffers, but I suspect its rare given the sizes likely involved that it will actually have a significant effect on a given program. Theres the standard rule of not trying to optimise before you need to.
Theres also bound to be a slight processor overhead, but this will be even less significant.
It all depends just how much it is used, if there are many large chains it could be a problem, but I think it unlikely to be a problem.
As David said it is likely an indication of poor design It would probably be more efficient for components to be able to share more complex objects directly, but its all down to specific uses (and I'm having trouble thinking of a reason that you would use multiple buffered streams in such a way).