To pull out a couple of the more provocative statements:
> completely invalidate Einstein's General Theory of Relativity.
Only in the sense that general relativity invalidated the Newtonian model. That is to say that the two theories had to agree, within experimental uncertainties, in domains where the Newtonian model was known to work. Where the Newtonian model was known not work, such as the discrepancy in the precession of Mercury's perihelion, is where general relativity has value. It can be argued that dark matter is general relativity's analog to the precession of Mercury.
> That would completely break modern Physics. Right?
No. It could alter certain parts of modern physics, but it can only do so where the observational evidence contradicts current theory, current theory is supported by weak evidence, or the evidence is incomplete. The important thing to realize is that physical theory is based upon mathematical models. Mathematical models are predictive, and observations can be made to support the model or disprove it. Even then, claiming that observations can disprove a model is too strong. Contradictory evidence in one domain does not automatically invalidate supporting evidence in another domain (though it may encourage people to go back to examine the validity of that evidence or improve the accuracy and precision of measurements).
It is also important to consider that a mathematical model is an approximation that must agree with observations within uncertainties. As such it is possible that multiple models may fit the observations. Part of the reason why we look for models that predict something new, such as Eddington observing the deflection of light as predicted by Einstein, is seek an understanding that accomplishes something more than fitting the data. The ability to come up with new theories that fit the data is also why we are hesitant to adopt new theories when there is a discrepancy. When it was discovered that the precession of Mercury did not fit the Newtonian model, there were efforts to seek out explanations that fit the Newtonian model (e.g. is there a body perturbing the orbit that hasn't been previously discovered). General relativity's ability to predict the discrepancy in the perturbation was wonderful, but the deflection of light by gravity (a previously unknown effect) is one of the bits of evidence that allowed us to say general relativity is true since we are now confident that the inability to find a body perturbing Mercury's orbit is because no such body exists.
It should be noted that none of this is meant to claim that a better theory will replace Einstein's, simply that any new theory cannot overturn what we already know from general relativity.