It was not showed experimentally - the only experimental evidence of gravitational waves is that some binary pulsars change their orbiting frequency exactly as expected from their losing energy by gravitational waves of the GR-predicted intensity.
However, it is surely established theoretically. The answer is Yes, gravitational waves that carry enough energy and squeeze it to a small enough volume - essentially the volume of the Schwarzschild black hole whose radius $R = 2GM/c^2$ is calculated from the mass $M=E/c^2$ where $E$ is the energy carried by the waves (the numerical coefficient $2$ is not necessarily accurate) - inevitably collapse into a black hole. In fact, a collision of two particles with high enough energies is enough, too. The conjecture due to Thorne that the squeezing of the energy is enough is known as the hoop conjecture.
This fact can be numerically calculated by simulating general relativity on a computer. The process in which high-energy collisions of particles - not only gravitons - lead to the birth of black holes is also the dominant or universal scattering effect at huge, trans-Planckian energies (when the energy of a particle is comparable to the lightest black hole or higher).