Well yes, but no 
When we get to the point when there are no more Conan Exiles servers, it’ll be either because Funcom went bust or because they shut down Conan Exiles because it’s not profitable anymore.
Let’s ignore the case where they went bust, because it’s actually easier to handle, and focus on Conan Exiles being shut down. Your game should work as long as Funcom keeps Funcom Live Services running and using a protocol that is backwards compatible with the last-CE-update-before-shutdown.
TL;DR: DRM is bad for consumers, but we’ve already known that for years and it’s not going away 