Are weighted games in Goko Dominion adventures winnable by sheer strategy?
There have been numerous threads discussing this topic on the Dominion Strategy Forum, including this one. But, to boil it down, it seems like the answer to your question is "no, some levels are essentially unwinnable without using zaps". I think that all of them are beatable if you just use enough zaps to bring yourself back to even starting decks with your opponent, but many aren't beatable without using zaps.

One money quote:


  I would not try those levels with no zaps. You get free zaps though, usually five. Just click on cards to zap them. It's a decision as to what to zap - although using three on Provinces is mostly automatic. At first I was upset by it, but I mean, in the end it's a variant and there's nothing especially wrong with it.
  -- Donald X.


In addition, there appear to be ongoing efforts to modify/improve the adventure campaigns for better balance, and to create additional adventures. Current status of these efforts may vary. This being said, some reliance on zaps in most adventures is probably going to remain.