Only if you can detect and hit them. Cruise missiles are small targets and fly NOE, and modern ones are stealthy as well,
Not all cruise missiles, but the US TOMAHAWK for sure was designed with that in mind. They fly exceptionally low to the ground, typically below RADAR coverage so are practically invulnerable to defensive systems.
Hypersonic missiles were only practical for use as delivery systems for nuclear weapons, and the US abandoned the concept once SLBMs and ICBMs came onto the scene.
Something that almost everybody should be aware of, and that is non-ballistic hypersonic missiles can only operate at high altitude. The exact same reason the SR-71 and X-15 operated at extreme altitudes at the edge of space. Craft traveling at that speed build up a hell of a lot of heat. And the lower the altitude, the more heat they build up. That is why the SR-71 only reached the confirmed speed of MACH 3.2 when it was in excess of 80,000 feet. And even at those altitudes, the craft got extremely hot and would expand in size.
Try doing MACH 5 at lower altitudes,, and you are going to have a very pretty low altitude meteor before it burns up due to atmospheric friction.
For some reason, people simply love to put amazing capabilities on things they simply do not understand. Like the claim that such equipment is also "more maneuverable" at hypersonic speeds, even though the exact opposite is true. Or that they are "impossible to detect", even though once again the opposite is true because of the extreme altitudes they operate at.
Sure fire ways you can tell somebody is either spewing propaganda, or simply making things up as they go along.