Yes, the 'Update Collection' feature does enable to you choose more than one tag.
You can set tag-based automatic badges, that get applied to products which have a specific tag added to them on Shopify admin (here's more on how to do that).
This means at a time, you can enable auto-application of badges to products part of a multiple tags and/or single tag.
Products that are tagged to any of the <tag name/s> tags will have the respective badges appearing automatically
Here's a step-by-step guide to enable auto-application of badges based on tags.
For further help, please reach out to us via the in-app chat or drop an email to [email protected].