It depends. The main use of react helmet (not to be confused with express helmet for node.js) is server-side rendering. Even in an SPA you may want to do server-side rendering, in which case helmet will likely be useful.
But if you're not doing any SSR, there's no point in using helmet. You don't want to render into the html <head> directly, instead you probably want to generate <style> elements when modifying CSS at runtime (e.g. using a library like styled-components which does this automatically) or you want to access the document.title directly. Everything else can likely be determined statically and added to your HTML before it is served to the browser.
Helmet is also useful for dealing with meta tags used by social networks and search engine crawlers (i.e. SEO) but there's no guarantee those will reliably run the entire application before looking for these tags, so I wouldn't worry too much about this until you need server-side rendering.