Do WordPress Tags Help SEO?

Short Answer: No.

To elaborate, Google's proprietary search algorithm is something that it keeps top secret. However, the company has provided general guidelines for developing Web content that is indexable, and third-parties are constantly experimenting with Google's search functions in order to understand them better. The consensus is that Google puts useful content at the top of its organic search results. In this light, tag spamming on a WordPress site creates clutter and reduces usability, so websites where these types of keyword spamming methods are employed will be less likely to be useful to its visitors and, therefore, will perform worse in Google's search rankings. So, make your site a place where people will find what they're looking for, where they'll want to spend a few extra moments browsing at other things, and where people will want to come back to, and the search engines will (in theory) rank your site accordingly.