of course you can ask. but, as you guessed doc will say no. first because your insurance will not likely pay for him for it, and second, mainstream medicine believes that a "diseased" gb can not recover (which is untrue- you just have to change the factors that lead to the stone formation).
re the first point, its a money issue. no way will your insurance co pay for it, but, if you used your own money doc might do it. problem is, unless you change the things in your life that lead to stone formation, the stones will come back. diet, exercise... and also very important stress. just removing your gb will not change the negative impact these factors are having on your health. the gb is just the tip of the iceberg... gb don't "malfunction" for no apparent reason... our lifestyles cause it and cause a lot of other probems we tend to want to ignore.