Do back links take effect immediately after indexing?

Google doesn't know what links generate traffic. They can only measure this via Google Chrome and Google bounce rate, but it's hardly viable to rely on that. Google can't, and doesn't have a monopoly on the tools people use to navigate the web. User engagement has 0 impact. It can't have an impact. What Google does is approximate user engagement.

That's what anchor tags are for, link placement, and those things.

As long as the backlink is good, it should have an effect almost immediately. Depending on how strong the link is, your current backlink profile, you might, or you might not see an effect. The link is however taken into consideration as soon as it is indexed.

/r/SEO Thread Parent