If you don't give them some kind of success to cling to, my concern would be a level of hopelessness so intense, they just give up. Basically, I would want the PCs to realize that while perhaps they cannot always save the world, they can make a difference in it.
There's another way to do this... Run the adventure as a sort of 3 Act adventure.
In Act I, you set the stage... A small island (find one just off the coast somewhere, with a quaint little village on it) completely vanishes off the face of the earth -- disappeared without a trace. That's the trial run for the Deep Ones. Investigation into the disappearance of the island will reveal clues that point toward the ritual, and toward Chicago as the next target.
In Act II, things look bleak... Despite the new trail, it's already too late to save Chicago. At best, a warning might get the city evacuated in time, but who's going to believe such a story? If the characters act fast, though, they may be able to find additional clues the suggest that Chicago isn't the only target.
Now, in Act III, while they couldn't stop the destruction of Chicago... Perhaps they can stop the destruction of other cities. How many more cities will vanish, before the players can put an end to the madness?
In the end, the PCs will have success of a sort, but it's a costly, world-changing success that leaves millions dead and at least one major city completely destroyed.
Something else to think about... A major city simply ceases to be. What are the various governments of the world likely to think about that? Perhaps the resulting international political situation may overshadow what happened to Chicago?