In order to have a democracy, you have to be able to count the people being represented. You have to prevent ballot-stuffing and its equivalent, population-stuffing. If you don't do that (or don't do it well), you have a system that will be open to as much criticism for being fake as ICANN gets for being closed.
Somebody has to define who is, and who is not, in the constituency. So far, that's been done with hand-waving.
So, if ICANN cannot survive without an At Large constituency, but that constituency is susceptible to nearly-trivial problems of representation, then ICANN wil die as soon as people see the problem.
Well, maybe not. ICANN hasn't died even though it is vey clear that there are huge problems with transparency. Having no real democracy from the AL folks might turn out to have as little effect.