I drove from Upstate NY to Anchorage in 1976 with a 1975 240D, the first new car I ever bought. No problems, and back then the road was, as someone noted above, all gravel except for a few miles on either side of Whitehorse.

If the car is performing very poorly, meaning you have too little power, check the throttle linkage carefully. These cars have a series of levers that turn the throttle movement of your foot to a twisting motion that moves the fuel controls on the injection pump using a linear motion. There are a couple of prime spots where the linkage can get loose and you lose up to a third of the available, and necessary, throttle motion at the injection pump. I have repaired this on my 1982 and 1983 240D (the 1982 is dead and being readied for the scrap yard) using popsicle sticks and electrical tape to take up the slack in one of the joints.

Good luck and enjoy the drive. I also made the trip once in a 1967 Fiat 124 Sport Spyder, in late February. The road was much better, all solid, smooth ice. But it was mighty cold. Jim

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Own:
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

Owned:
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)