I dont think so. Everyone would have to posess the same mods or you load up your server with all mods and it randomizes them.
Well, my problem is when i use the mod my friend sees unrandomized version of my car (we both have Part Randomizer mod)
It sort of works, if you go into a vanilla, public server and randomize your car, you may have to save it and respawn it for others to see it- as long as the parts are also vanilla.
I tried doing that - for other people, my car was unrandomized even after i saved and loaded the config. (it was all vanilla) But maybe that was because i was doing that on my own server that had some mods, gonna try that out on public vanilla server.