General relativity vs graviton discovery

Does the discovery of a photon and development of quantum electrodynamics make Maxwellian electrodynamics redundant? Not a bit.

Each physical theory has its domain of applicability. Electrodynamics successfully describes the macro phenomena of electricity and magnetism which are very much obscured when you look at them from the point of view of QED. Honestly, it is not so simple to derive even Coulomb's law.

One might say that QED encompasses everything Maxwell equations do, but in most cases the Maxwell equations will be more practical. On the other hand, QED is designed to solve problems that Maxwell equations can't solve.

The similar thing will most probably happen with the graviton. General Relativity is an amazing theory that is tested on the scales from our daily life to cosmological ones. We haven't seen any deviations from it yet, but we expect it to fail at some point — at small distances and high energies.

But development of a more fundamental theory won't make GR obsolete. For the same reason you still use Newton's equations.

If the graviton is detected and its cross section and other properties and interactions are measured well find out something about quantum gravity and maybe even how to unify gravity and the other forces. As @CuriousOne says we are pretty far from discovering it, nobody is looking for it, and we don't have any way of even coming within 10 orders of magnitude of having the energy to probe the sector where it might be possible to see it.

Without a good quantum gravity theory we are also a little blind in any search we might do, know little about what to look for. We know it should be spin 2, no mass, interacts with all matter sort of the same way, and almost nothing else.

General Relativity has been proven. If at much higher energies something diverges fro GR, it does not make any difference, GR is known that it does not apply to those energies (and such small sizes, generally thought to be the Planck energy and length)

Nothing to worry about except that quantum gravity nobody yet knows what it is.

In a quantum world, all oscillations are quantized (if they are truly periodic, not just approximately periodic). For example, oscillations of a solid are quantized and the quanta are called phonons. That doesn't mean that the model of the solid as a lattice of (quantum) atoms is wrong, or even that it's an approximation with a limited domain of validity. On the contrary, it is exactly right, and it predicts the existence of the phonons.

Fundamental (as far as we know) particles like electrons are oscillations of the fundamental field of the Standard Model. They are quantized for the same reason as any other oscillation, and we call the quanta particles, but it is the fields that are fundamental, not the particles.

Gravitational waves are oscillations of spacetime, and should be quantized for the same reason. The rules of quantum mechanics don't (and can't) distinguish between different kinds of oscillation. All that matters is whether the system returns to the same state at different times. If we manage to show experimentally that gravitational waves are quantized, that doesn't mean that there's anything wrong with the geometric picture of gravity.