To answer the question, a comparison is convenient with the phenomenology of the Hawking radiation to make evident some crucial differences.
First of all, what actually happens for an accelerated observer moving in the Minkowski invariant state is that this state appears as a thermal bath with respect to the Rindler Killing time. A thermal bath is different from a radiation state: the former is an equilibrium state, the latter is not.
Strictly speaking the phenomenology is different from the one of an observer in the spacetime of a large black hole observing the Hawking radiation exiting from the horizon. There a net flux of particles exiting the horizon exists (with thermal properties with respect to the Schwarzshild Killing time) and nothing enters it. That is quite different from an equilibrium state, in fact the black hole eventually evaporates!
This situation, in the Kruskal extension of the Schwarzshild spacetime, is described by the so-called Unruh state of the background quantum field.
Conversely, what describes a thermal bath at the Hawking temperature is the so-called Hartle-Hawking state. Here the flux of particles entering the horizon is equal to the one of particles exiting the horizon.
What happens in the Rindler wedge for an accelerated observer in the Minkowski vacuum is an approximation of the phenomenology of Hartle-Hawking state (in accordance with the equivalence principle) and not of the Unruh state.
A crucial difference, distinguishing black hole phenomenology from Rindler phenomenology, is however that the particles of HH and U state around a black hole are standard particles. In the sense that, far from the black hole where the spacetime becomes flat, they are described by modes of standard QFT in flat spacetime.
Conversely, particles used to describe the thermal bath for the accelerated observer are Rindler particles without physical direct meaning. Their existence is furthermore confined to the Rindler wedge, so that their physical relevance is disputable. This does not automatically means that the abovementioned thermal properties do not exist since different theoretical descriptions of extended thermal states of a quantum field are at our disposal, in particular, the one relying on the KMS identity.
In summary, there is no experienced radiation of Rindler particles for an accelerating observer but a thermal equilibrium state of those particles takes place. A quantitative description of the effect of the action of this bath on physical devices is more difficult.
In particular, the geometrical setup is a delicate matter here: the rest space of the Rindler observer appears to be homogeneous, but the norm of the Killing time used to define the thermal equilibrium depends on the spatial non-Cartesian coordinate usually denoted by $\rho$. Therefore to quantitatively answer your question one should fix suitably adapted definitions.