Sorry, Product Customizer hasn't learned this trick :( Product Customizer is best used for customizations or options that don't require inventory tracking or their own unique SKUs.
We do have this on our idea board though -- If you'd like to vote for this feature, please let us know. We'll add your email to our voting list, and we'll also notify you if we start to build this feature.
It should be noted that Product Customizer will not interfere with your ability to manage inventory or SKUs for your products; we just cannot manage them per option from the app. For example, if you use Shopify variants for some of your options, but use Product Customizer to add a monogram, etc., you can still track SKUs / inventory for your variants. We just cannot do so for options added via the app.