I've not driven an SLK in Alaska, but I have driven in Alaska and, while some roads are indeed little better than tracks the major routes are pretty much the same as you'd find anywhere else in the USA. Vehicles clean the roads by picking up or kicking away debris so anything that is reasonably well trafficked should be fine.
One good thing about the SLK is that all the forward panels just unbolt. The front bumper/fender is very cheap (in the UK at least) and comes pre-painted from the factory if required. And it's the whole nosecone - all the way to the bonnet/hood. Likewise, any stone damage to the hood or front wings should be relatively cheap to repair. The roof glass could be damaged by a BIG stone but so long as you're driving with the roof down (and wearing a helmet) you'll be fine, get a white helmet and tell everyone you're the Stig's Yupik brother
I've not driven in mainland Alaska, either, though I have in the Aleutians! Highway 97 up through British Columbia all the way to Dawson Creek is paved, and I've been on it as far as Prince George--very good road. The Alaska Highway (or Alcan, for those of a certain age) is now paved all the way through as well. Check out the website for The Milepost, which is the authoritative guide to road travel in Alaska at The MILEPOST: Alaska Travel Guide and Trip Planner., which as they say is the bible of north country travel.
One thing to bear in mind is that "paved" doesn't mean autobahn-smooth in the far north, as any guidebook will tell you. It ranges from great to terrible, and since the harsh environmental conditions necessitate frequent rebuilding, there's a great likelihood of encountering stretches of gravel in areas being worked on. I want to drive it as well, but not with the SLK. If we get a GLK diesel in the next few years, that will be the car of choice for us.
I've done the trip in/on everything from a Goldwing motorcycle to an eighteen wheeler. It is certainly doable in a SLK. If you come now you'll be fine so long as you don't push your fuel reserve, they don't joke when they say 300 miles to next gas station. I wouldn't recommend it earlier in the season for the mentioned reasons of debris on the road way. The Milepost guide is a must! Some of trip is monotonous, some of it is spectacular; it is an endurance test anyway you cut it. If you make it as far as anchorage, look me up; there are some wonderful sights and eats.
I didn't make it to Alaska, but I did manage to drive 10,000 solo miles.
Dade City to Ohio, back to Lexington KY, westward on I-40 to Amarillo TX, up through Death Valley to Yosemite, Reno, northward to Glacier National Park, Moose Jaw, Winnipeg, Sioux Falls SD, St Louis MO.....and then back to Dade City.
Oops.....I almost forgot the highlight of the trip.
....and my trip theme song....
Many times I would return to the car and find folks standing around it. I just figured they were wanting to see me..........until I saw the Cowboy sign in a store.