I own this game for more than a year, and have launched it occasionally. It never launched my browser. It never displayed an ad. What website was launched specifically, and which ad was allegedly displayed?
From the first page of Steam reviews: Adware was added to the game by the new publishers Topshelf, graphics aren't working correctly, GoG version works correctly without Adware, Valve should be ashamed to let this tripe adorn their shelves. 1/10 When you start this game, it opens a web browser and brings you to the Steam page for Raven's Cry. They're advertising for another Topware game by employing pop-up advertising. You're greeted with a redirect to your browser telling you to BUY PIRATES COVE everytime you load up the game Game seemed ok the ~6 minutes i played it, but i can't condone a game that contains an adware that opens up your web-browser and redirects to the store page for another game. Opens browser on it's own in the background, supporting game developer's new game.
So it looks like you should hesitate to update your own copy, if given the option.
Then again, another (more recent?) review says this: THERE IS NO ADWARE IN THIS GAME. THESE MANY REVIEWS THAT SAY SO ARE OLD, AND HAVE NOT CHANGED EVEN THOUGH THE ADWARE HAS BEEN REMOVED.