In Zen Cart the "products_id" is used to uniquely identify each product (think of this as a Zen Cart specific product SKU). This is used internally by Zen Cart to track inventory, manage orders, etc.
It sounds like you want to use a 3rd party software (such as QuickBooks) to manage your inventory... And in your 3rd party software you are identifying products by "model" (and not by the Zen Cart product SKU) ...
If this is the case, you will need to find additional software to integrate (and provide synchronization inventory / data between) the two pieces of software involved. Most well written synchronization software will be able to MAP the Zen Cart product SKU <==> the 3rd Party product SKU.
NOTE: Of course a poor man's solution may be to alter the database table "products" changing the index "idx_products_model_zen" to unique (enforcing unique model numbers at the database level) and the column "products_model" to not allow NULL values (forcing products to have a model)... But this will complicate the upgrade process in the future... And one will still need to synchronize the inventory model, status, quantity, and other data between Zen Cart and the 3rd party inventory management software... Either by hand or using another 3rd Party tool for integration...