Hi @robertopage ,
I take a look at what you concern, and found this article by Shopify explaining about their tagging system: Creating and using tags in Shopify · Shopify Help Center
Basically, from what I've found, inventory tags can only help you to search your products and also help your customers to search within your online store. However, tags won't be considered to up rank SEO. For SEO, you can watch this video to learn more how SEO works for Shopify products: https://youtu.be/AnpWO2YzmU0
I also attach a summary image about the SEO elements that you'll need to pay attention on for Shopify products here:
Hope these information are useful, let me know if it helps!