Product tags alone don't do much for SEO. They are just a way to organize products inside of Shopify. ... To get back to their question, yes product tags can help with SEO but really, they are just treated as content by Google. And more content is always better as long as it's quality content.
The words that are used in Tags are also called keywords and all organic searches are made on keywords. The whole SEO campaign is run on the foundation of keywords.
When you tag all of your topical headings throughout the post, you tell search engines exactly what your content is discussing. This is how Google creates the snippets you'll sometimes see when looking for a topic.