I think that Calvin would get a female voice actress who can do boy voices well. Think Nancy Cartwright, who most famously voices Bart Simpson. As for Hobbes, I could see someone like John Candy of all people providing his voice, since he had this very warm, yet sarcastic type of sound to his voice.
If the special aired in 1988 or so, I think it'd definitely increase awareness of the strip for sure. Perhaps the success would lead to Watterson reluctantly licensing Calvin and Hobbes for some toys, games and clothing, but only if he gets full approval on the products. I'm not sure if the strip would reach Peanuts level fame, but perhaps at least Garfield level.
I could see a few more specials airing during the early nineties, until Watterson finally gives the okay for a TV show. It could run from 1995-2000 and air on Nickelodeon. Because John Candy would be dead by this point, I think they'd use Tom Kenny to voice him instead. Nancy Cartwright would still provide Calvin's voice. I could see about 5 seasons and 65 episodes being produced.
The actual strip probably would run longer, since Watterson would realize he has a lot more stories left in him and since the strip is much more popular than it was in the OTL and he'd want to give children more of his work, so long as he'd have good ideas, which I think he would.
After the show ends in 2000, I could see the strip ending in about 2003 or so, perhaps 2004. That said, I imagine that it would be much better known around the world and there'd be demand for a movie. Watterson would spend most of the 2000s painting and giving interviews every so often, as well as occasional public appearances. I don't think he'd have a problem with Calvin and Hobbes being licensed by Viacom to be featured at Universal Studios, so you could see Calvin and Hobbes walking around in the park, along with a ride themed after Spaceman Spiff.
I think that the strip's popularity would fade a bit in the 2000s, though the series and merchandise would have a devoted fanbase. I think a few video games could come out during the Nick series' run, with playthroughs of them becoming really popular on YouTube.
By the 2010s, with the rise of social media and the internet, the strip would start regaining popularity and petitions would be signed by fans across the world to bring back the strip and get the movie greenlit. While Watterson initially would be unsure and would make it clear that he'd be against restarting the strip only due to popular demand, he'd probably relent after realizing he has enough ideas to revive the strip. In 2013, Calvin and Hobbes would resume production and fans would be very happy. The movie would be greenlit around this time, to be released into theaters in 2016.
How does this sound?