Based on research I did when I was considering doing a straight-out exhaust on my 300d, you will need to make sure your pipe terminates at least 1" out beyond the rear bumper, to get rid of that boom at higher speeds and on hard acceleration.

To answer your main question, on a previous 300sd that I had, the exhaust rotted and fell off midway under the car and due to my underemployment at the time, I had to drive it that way for about six weeks. The only issue I had was that the insulation and rubber seal were long gone from my shifter opening in the console so when stuck in traffic, or when driving with the sunroof open, I got exhaust coming in the car. The engine on the car was tired so I wasn't the nicest diesel you could imagine.

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Mac
2002 e320 4matic estate│1985 300d│1980 300td
Previous: 1979 & 1982 & 1983 300sd │ 1982 240d

“Let's take a drive into the middle of nowhere with a packet of Marlboro lights and talk about our lives.” ― Joseph Heller, Catch-22