I think I'm becoming quite neurotic about speed and mobile user experience at this point for a super bootstrapped MVP I'm building but I still feel...
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Yes, service workers load from cache making any site faster than without, making the cached assets load nearly instantly. Though they won't help with content updates--Wordpress is dog slow generally. I've done minor performance work on a project or 2 there going from 6+ second load times to under 1s as I remember. Generally it is a product and platform to avoid unless it very specifically addresses some business need.