Yes, after they are sorted by their individual sort orders. (And if all have no sort orders, then they effectively all have the same value: 0 ... meaning that only the secondary alphabetical sort by product name applies.
1. Leave Admin->Configuration->Product Listing->"Display Product Listing Default Sort Order" blank.
2. Edit each and every one of your products and give each one a sort order, based on the order in which you want them to show up.
Now whenever they show in a product listing, they will appear in the order of the sort order you supplied for each product. If there is more than one with the same sort order value, then the product name will be the secondary sort, in alphabetical order.
Or if you'd rather write custom code to change how the SQL pulls products from the database, you can do that too.




