The best way to sort out correlation versus causation is by a random experiment. Let some high rep user who generates a lot of questions pre-commit to, before the next 20 questions they ask, flip a coin and ask either under their own login or as anonymous. I did this with answering questions here and concluded that, if there was an effect, it was smaller than the variation within answers.
Unfortunately for the proposed experiment, very high rep users don't seem to ask a lot of questions! Among the 10K+ crowd, I think no one has asked more than 30. This is an interesting contrast to MO -- I believe MO started in Oct 2009, so 22 months ago while math.SE started in Jul 2010, so 11 months ago. That would suggest that high rep MO users should have roughly twice as many questions as high rep math.SE users. In fact, the ratio is much higher than that. I didn't collect data carefully, but it is quite common for a high rep MO user to have more than 60 questions, whereas a high rep math.SE user never has more than 30.
If someone down around the 3K or 5K range wanted to do the experiment, it would probably
still be interesting. Any volunteers?