No, we still can't believe it either, but for now at least, Hopper appears to be dead. He fights with the Terminator wannabe Russian operative who killed Alexei on the landing next to the machine that the Russians built to open the gate. While he manages to push the operative into the machine, killing him, Hop also traps himself on the landing in the process. Knowing there's no way to get back behind the safety of the glass where Joyce is waiting to turn the keys that will destroy the machine, he gives her a sad nod to turn them anyway, leaving him with little to no chance of survival.
It should be noted that we don't see Hopper disintegrate, and there is a postcredits scene that reveals there's an unknown American in the Russian prison three months after Hopper's death. But for now at least, we have no choice but to believe that Hop sacrificed himself to save his family, friends, and ultimately, the world.