I sell on Etsy and tags I use there get my listings in the search results, there is also a limit of 13 tags on Etsy. Here on Shopify there is no limits for tags and I consume a lot of time adding them in each product. Are the tags in shopify help with SEO or help just organize your stuff? If they help with SEO, how many do you add? Please let me know as if they are not relevant in SEO I will not lose time with them.
Short answer: NO!
Product tags are only used for organizational purposes and they won't help your SEO rankings.
If you really want to use keywords, you can include these in the products title & meta description.
Hope that helps.