Theoretically, Yes. Relativistic jets accelerate beams of plasma, so  due ionization it has a lack of baryonic matter as @Uhoh pointed, instead it contains a lot of leptons and antileptons like positrons. But there is a possible scenario covered in [research papers][1] that maybe baryons arising from the accretion disk could be injected into the jet which so as appears in X-ray binary, 4U1630-47. I agree the paper might no be so assuring but there is a well enough chance of baryonic matter in a jet. Even if it is not there minute interactions with the interstellar medium and surrounding could in theory inject baryons into the jet. As to how the relativistic jet could cool traveling  at 2/3rd the speed of light through inverse square law eventually it would disperse in the surrounding and cool to form dust particles, it could also cool through **inverse compton cooling**.

As for could we detect flashes of radiation when dust speaks smash into meteoroids at relativistic speeds?, Yeah the impact flash, could create tiny peaks of radiation but it would be very hard to detect such radiation because it wouldn't be intense enough to travel to Earth considering inverse square law.


  [1]: https://ui.adsabs.harvard.edu/abs/2013Natur.504..260D/abstract