Once you delete an asset then yes, eventually, Google and other search engines will notice this and remove it from their index.

However, Voice has no control over this, and search engines can sometimes be pretty slow at removing things. I would expect it to take a couple of weeks at least.

If you have your own domain name, then you can register this with the Google Search Console and use this to remove old pages from their index, and to request indexing of new pages.

(You can't do this if your site only has an e-voice.org.uk URL, for hopefully reasonably obvious reasons!)

Any site can add a custom domain name at any time, which if well chosen can certainly help with search rankings!

Thanks

Joe