I think when used sparingly (ie. not cramming your tags full of everything your blog is about, but keeping a tight-reign on the true relevance) then it can help with interlinking the site and will in turn, help the search engines decide what your true “specialty” is in your topics.
For example, let’s say you’re working on a personal journey about weight loss – and you tag your daily food journals with “calories, food journal, fat grams” and that’s the majority of what you post to the site, then the search engines will conclude that your site mainly relates to “calories” “food journal” and “fat grams” – so yes, it will help in SEO…
However, I do know that the search engines won’t place a HEAVY rely on these. It’ll help, but I don’t think it’ll hurt if you don’t use them, given the nature of WP and how it basically interlinks things by category and such anyway.
There’s a lot to SEO – a LOT. Every little thing you do (or don’t do) has just a small effect either way. So if anyone’s thinking that this will boost your rankings and you won’t have to do anything else, they’re sadly mistaken.
In my company, our motto when working on SEO is “Fly Low Under The Radar” – the less obvious you try to be, the better. And that motto hasn’t failed me in nearly 5 years now… ??