Someone asked about this same situation with the retail version (
here) and it was confirmed they would be able to install the game on a PC that did not have internet access.
I don't recall if anyone has specifically mentioned getting DKS from the Larian Vault (or re-downloading it) after the DRM free executable was released, but it would very, very strange for Larian not to update their own version of the game. If they didn't want to remove the DRM they would not have made the patch in the first place, and did all the paperwork required to get publisher approval for its release.