No. They're not setup to be a principal route between two nations and most satellite networks until very recently didn't even route messages through other satellites but instead retransmitted them to a ground station with access to hardline internet. Even Starlink mostly does this still because it's way cheaper and easier.

You can see an unofficial tracker [0] of the Starlink downlink network and see how outside of some rural areas your data is only moving a few tens of miles away most of the time before it's sent down to a ground system. Their sats have 3 200 Gbps laser communicators for intra constellation routing which is pretty small for the task of replacing fiber optic links.

[0] https://www.google.com/maps/d/viewer?mid=1805q6rlePY4WZd8QMO...