From the game info box:
This game may present an endless loading screen, although starting the game while disconnected can prevent this.
People have earned achievements as recently as December 2017 so the only ones that should be discontinued are the ones requiring upload/download from the Disney Infinity servers.
The achievements that have the external content flag required you to download certain toyboxes to access certain items for the achievement, so those probably can't be earned unless you already completed that part of the requirement.
Game On.