Although maybe you would be making a mistake....
http://poetsandquants.com/2016/09/22/highest-paying-mba-programs/
With a degree from the best MBA program in the country, at mid career, the median salary is $201k. That is over $250k less than the median anesthesiology salary listed in MGMA. The odds aren't in your favor if you want to head a different direction with your career (current trends in medicine/anesthesiology notwithstanding).
However, if you are going to try to use your medical degree too and go for CMO, the median salary is about $475k, which is only $22k more than the average anesthesiology salary but presumably doesn't involve call or weekend. Is that worth 2 years and $100k plus opportunity costs to obtain from a top school? I'm not sure, especially since an executive MBA from a top 20 program and 10 years experience will probably make you an equal candidate.
Things are still good in anesthesiology, although the writing is on the wall. May as well make hay while the sun shines, and go for an executive MBA while you work once you are BC.