Is it possible to alphabetize a sorted view?
It is definitely be possible to add a second sort to the query which will give the desired effect, but you will have to write some custom code.

There are several hooks that Views provides that you can use in a custom module.  I suggest looking at hook_views_query_alter().  The example code on the API page actually shows it altering a WHERE clause, but creative use of dsm()'s will help you figure out what you need to change.

I'm sorry that I can't give you code (because this kind of modification is highly specific to your installation), but this is definitely the way to go.