Is a laser wire a non-invasive method?

A tightly focused laser beam (laser wire) is used for measurement of transverse electron beam sizes in storage rings and linear colliders. It is assumed that the laser beam does nothing with the electron beam except Compton scatterings which happen with a rather small probability. In reality, electrons crossing the laser beam get kicks (with 100% probability) proportional to the square of the laser field and inversely proportional to the beam energy. In practical cases of beam diagnostics this effect is negligible.