You can if you recompile wubi with a custom Mint ISO according to the wubi wiki. You would probably still have some problems afterwards because of the subtle differences between Ubuntu and Mint. I don't know enough about wubi to help.
"The only thing necessary for the triumph of evil is for good men to do nothing." Edmund Burke
I have not studied wubi - you have to limit yourself somewhat.... I'm not sure of the outcome as there are differences, not big but remember man and chimp has the same DNA to 98 % or so. It will not be included with Mint because of the differences....
Don't fix it if it ain't broken, don't break it if you can't fix it