DT_RPATH does, but DT_RUNPATH does not (and is why DT_RPATH was deprecated). You can see what is being used with readelf -d $library and looking for the DT_ key in use for the paths.
Nope. LD_LIBRARY_PATH is a blunt tool and affects an entire process tree. I would recommend setting the RPATH in the simulation code to stick to the ParaView it was built against (at least by default).