Yes, the crystals power the Death Star and are "drained" in the process, as per the canon Rogue One prequel novel
According to the databank at the official Star Wars web site, the answer appears to be yes.
DEATH STAR SUPERLASER. Each of the Empire’s Death Stars was built around a terrifying weapon — a superlaser array capable of destroying a planet. According to legend, the ancient Sith used massive Kyber crystals to create superweapons; during the Clone Wars, the Geonosians revived the superlaser design. The Empire constructed the first Death Star in secret for nearly two decades before using it to destroy Alderaan; the second Death Star boasted a more powerful superlaser, with improved targeting sensors and power regulators.
I take this to mean that the Geonosians made a design for a Kyber-based superlaser at the bequest of Palpatine, whose was inspired by ancient Sith legends of massive Kyber-powered weapons.
Furthermore, the canon Rogue One prequel novel Catalyst appears to explicitly mention that the crystals power the Death Star, rather than simply focus it. From a review of the novel:
The parents of Jyn Erso (Felicity Jones) don’t appear much in the film’s promotional material — and don’t expect them to show up for very long in the movie itself. But Catalyst centers mostly on the elder Ersos and how they navigate a professional relationship with Imperial commander Orson Krennic (Ben Mendelsohn) as the Death Star begins construction in secret. Galen (Mads Mikkelsen) is a truly brilliant scientist, plucked from a remote world to receive a top-notch education. His fascination with Kyber crystals — the type that power Jedi lightsabers — gives rise to a theory about how to provide endless sustainable energy to power planets across the galaxy. But as was suspected throughout production on Rogue One, Kyber crystals are also what power the main weapon of the Death Star. Galen’s research gets twisted from innocent energy applications to more sinister ones, and it’s that process which leads the Ersos to flee, setting up the flashbacks to Jyn's childhood in the Rogue One clips.
And now for direct quotes from the novel:
"Galen Erso is one of the Core's most renowned polymaths....At present he is the preeminent authority on crystals and their use in supplying enhanced power."
"Containment," Galen said, finally composed enough to look at him. "The Kyber will submit to pressure up to a certain point before the output becomes impossible to harness. Untamable. Even this level of destruction is trivial compared to the raw destructive power the crystals are capable of unleashing."
Orson was still celebrating the fact that the power yield of the altered Kyber crystals had been amplified beyond any of his team members' expectations....
I would say this confirms that crystals themselves, albeit in an "altered" form, are the "fuel" — they are subjected to great pressure until they release the destructive energy that is channeled into the superlaser. Regarding whether they are "consumed", the novel mentions that they are
"drained of their inherent power"
by the process. In other words, the Death Star laser eventually leaves the crystals in a spent state.