I've read that solar wind consists of hydrogen atoms that are, near the Earth, travelling at about 450 km/s. This is only 3/4 of the Sun's escape velocity, but then the Earth is also 150 million km away from the Sun.
Does this mean that all those particles will eventually fall back down like a ball launched from a catapult? Even if said ball was launched at say 9 km/s, it's still less than the 11.2 required to escape so it'll eventually fall back down.
The escape speed at 150 Gm is about 42 km/s, namely $\sqrt{2}$ times Earth's orbit velocity of bout 30 km/s. This is vastly exceeded by the value of 450 km/s that you give, without reference. The conclusion is that the final whereabouts of the solar wind is not restricted by the Sun's gravity.
As to where the matter of the solar wind ends up, I would suspect in the Oort cloud but I give my conjecture for an expert opinion.
The experimental answer is simple: we see the solar wind flowing away, and we see no return flow. It is thus apparent that it is escaping.
It's a magnetized plasma: electromagnetic forces, not gravity, dominate its dynamics. It is thought that the primary avenue of escape is the heliotail.
Gravitational laws hold, and the solution for the trajectories of massive bodies are conic sections: Look at the answers in this question. There are stable orbits and trajectories that go off to infinity depending on the energy and momentum .
Particles in the solar wind can be modeled with fluid dynamics, having a mass per unit volume and the trajectory , of whether it will fall back or get on a stable orbit will depend on the energy and momentum carried by this fluid. So the answer for a single particle in the solar wind does not depend on its individual velocity but on the group velocity of the fluid and will have to be studied for the particular trajectory of the solar wind.
After all one expects theoretically for the particles on the earth to keep on going forever, or be dispersed if the current big bang model holds, or fall in not to the sun , but the center of the universe if the models of the big crunch turn out to be true.
Particles in the solar wind are frequently charged, and in the vacuum of space might remain charged for a LONG time. Such particles are affected by gravity, electric field, and take a curved trajectory in magnetic fields, like around Earth.
Small particles also are affected by light pressure, and having little mass relative to their surface area, are subject to repulsion from the Sun, due to incident sunlight. Rayleigh scattering deflects light, and also applies momentum to the particle.
The dynamics of solar wind particles are more complex than ballistics-in-gravity, and there's enough range in their speeds to cause nuclear reactions in the Earth's upper atmosphere. I'd expect those particles to end up... everywhere, including stuck to planets and thrown into interstellar space, and maybe even in stable orbits.
