It would be possible, I've made a couple of customizations in the past regarding this method. You need to know miniBB well and possibly understand how it could be connected to a 3rd party database
, if you are about 3rd party DB. Couple of miniBB core files like bb_func_login.php and bb_cookie.php should be adjusted to that.
However it doesn't mean users could register profiles without a username. Forums use a public name i.e. username to display in all threads and many other places. Displaying emails to public is unacceptable. So users should register/have a Username anyway. Further process makes logging via email not meaningful, because Username is involved anyway.