That's largely already a consequence of Schrems II.
If that third country has something like the CLOUD Act, then yes.
Actually it's pretty explicitly only about transferring data to providers which are under authoritan legislations.
It's actually already the case but everyone prefers to put their heads in the sand and hope for the best. It's not like we have real alternatives to AWS or Azure in Europe right now.
AWS/GCP/Azure are very keen on keeping the business in Europe, so they have European datacenters, try to keep them GDPR-and-other-laws-compilant, and will even sign a legally binding agreement with you swearing to keep all data on EU servers only.
Yeah they do that. But at the same time they have the patriot act law to respect, and the European privacy shield is dead. So right now it's challenging to know whether using Azure is GDPR compliant or not. Most people I talked with on this topic think it's probably not compliant, but they prefer to wait and pay a fine if necessary as they are not lawyers.
The Azure service fully operated by Deutsche Telekom seems pretty appealing right about now, but as far as I know they cancelled that. Maybe cloud providers will move to a kind of franchise model, effectively allowing smaller European companies to license an Outposts type software.
Ovh and scaleway?
Scaleway still lacks a lot of features but has potential on the long term. OVH lacks many features too, and quality.