The dye hues and dye stability would suffer by processing the film in C-41 as the developing agent is incorrect. In addition, REM Jet is removed from the back by a scrubber. If the carbon gets into the swollen gelatin on the front of the film during any processing step, it is locked in place and will leave microscopic black specs in the image.
REM Jet must be removed from the back only with a sponge scrub and then a wash before the film begins processing.
I have seen film ruined by the processing method described by Phototherm. At the time, it was others doing the job though. And, BTW, you may get by with an apparent good image from this, but the test is color quality, keeping of the image, and whether there are any microscopic white dots in the prints.