Not necessarily. It depends on the angle and location of impact. If it can be kept to one floodable apartment and the crew are still conscious enough to seal the doors then maybe, but if it strikes mid-bulkhead or at an angle such that it passes through several bulkheads, the ship is gone.
You're underestimating the size of the warhead. 1000kg or 2,205lbs is about 2.4 times the filling weight of a Mk84 2000lb bomb and RDX is about 40% more powerful that the tritonal in Mk-84s. So the blast itself is about 3.3 times that of a Mk84 plus the affect of 12,000lbs travelling at 5000ft/s.
There's a damn good chance that's going to trigger an ammo cache and produce a sh*tload of secondaries, which the carrier simply can't survive. If you think about it there's probably a few hundred aircraft bombs stored on the vessel plus missiles, plus fuel.
The USS Forrestal and the USS Enterprise were almost taken out when a weather cooked Zuni rocket decided it was time to go off. Similarly, a fuel explosion on the USS Kitty Hawk caused it to list.
Just because the ship can theoretically take hits to several floodable compartments, it doesn't mean that in practice when everybody is on fire and the ship is beginning to sink and secondaries are going off, that theory will prevail. Even optimistically, highly optimistically, a carrier hit by a Kh-22 will be going home for repairs and most of the aircraft on-board will be inoperable, which is a de facto kill in a war.