And the answer is: it all depends! As usual with human behaviour, it depends on the context.
Ophir, E., Nass, C., and Wagner, A. (2009) Cognitive control in media multitaskers Proceedings of the National Academy of Sciences of the United States of America, Vol. 106, No. 37
I don’t want to oversimplify the results from this careful study, so I recommend you read the article yourself. For me, it raises more questions than it answers, but it is a useful addition to our knowledge of information processing in information-rich environments. You need to make some large assumptions though before you can make the jump to teaching implications.