What I read in battlenet site, they said that the campaign progress is saved in server side with your profile along with your achievements.

So if you use other PC to play and login with your battlenet account, you should be to select CONTINUE campaign.

But in-game saved file will store locally in your PC, which means you can't continue your half way through match/game. For this, you have to copy the save file manually and paste at your other PC.

Hope this help, please clarify and comment if wrongly stated.