It would work. You can do a LOT with sort order - especially when you combine category sort order and product sort order. With sort order, YOU decide what order products appear in. If you want them to sort alphabetically when they are not truly alpha because of words like "The" and "An", using product sort order allows you to control that.
But with as many products as you'll have, it will be a labor intensive process done manually through the admin. It's a lot of work to set it up initially, but it's the only thing that comes to mind because I don't know of a way to make them sort alphabetically automatically.
If you find that's your only option, keep in mind that to avoid having to redo the sort order every time you add a new product, you'd want to set the product order as follows:
ABC's & 123's = sort order 10
Bears & Beanies = sort order 20
Cats & Dogs = sort order 30
This way, if you get a new product in called....Bubble Gum Squad, for example, you could set that sort order to 21 to put it between Bears & Cats and keep it as an alpha sort.
You may even want to leave as many as 50 increments between numbers to allow room for product expansion.
Once it's set up, it wouldn't be something you have to repeat again.
True, it would be a major pain to do it that way, but it's all I can think of. Perhaps there's an easier answer that is known by someone who has more experience with ZC than I do.
I don't know if there's a Mod for this either, have you looked through the Mods to find out?