My question has been closed for being off topic. The reasons are:
If you are asking a general question about what changes will occur in your life from playing musical instruments, this is out-of-scope.
this question is too broad.
yes, it is a simple question, but it needs to get more complex before it can be answered. You are looking for causation, right? That is difficult to prove without a major (randomly controlled) experiment. What does "more productive" mean? If you could reduce the bug-density in your code by 10% by practising the violin six hours per day, would you be more productive or less productive? That's setting aside "inspire my creativity" as even less measurable.
It seems to me that the mods want me to ask a question towards a study that I don't-yet-know, only then it is an on topic question.
But if I could ask such a question, I could have googled the answer, there is no need for me to ask here.
Also, the FAQ says that:
If you have a question about the accuracy of public claims made in the media or elsewhere, if you're interested in the evidence behind what you hear or read, then you are in the right place.
Don't you think that my question is perfectly valid for this forum?