From your description I would worry most about the likelihood the radiator hose will be damaged and fail while driving. In general, other than the extra shaking and vibration, running the car with worn out mounts is not likely to be catastrophic.
My daughter drives our 1982 240D and the driver's side mount failed completely - I mean it was split right through the rubber. The passenger side did not look as bad, but it was pretty much crushed. So, when the car was started the mounts would allow an inordinate amount of lifting on the driver's side. She did not report any problems until the car became particularly difficult to start.
In the end the starter had been damaged, and the exhaust mainfold fasteners were stretched from the constant beating, and I had to replace the starter, the exhaust gas recirculation tube, and the intake/exhaust manifold gasket in addition to the mounts. The car runs and starts better than it has in years, but the time with bad mounts probably cost me an extra two weeks of hand healing and a few hundred dollars (that little corrugated tube was $70!!).
I did not count any of that as catastrophic, but timely maintenance would have prevented at least some of the consequential damage. Good luck and hope this helps, Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)