This is probably going to happen, yeah. It will however likely also establish European companies as particularly secure and trustworthy.
For a long time already, it's been common practice to avoid Chinese services, because of the surveillance that the Chinese government does. And there's a growing number of people who avoid US-based services, too. The recent CLOUD Act certainly doesn't weakening their position either.
It also gives some non-eu based companies the same secure and trustworthy benefits. They just need to have an obvious presence in the EU, and not check if someone is in the EU when they are asked to apply GDPR.
For a long time already, it's been common practice to avoid Chinese services, because of the surveillance that the Chinese government does. And there's a growing number of people who avoid US-based services, too. The recent CLOUD Act certainly doesn't weakening their position either.