Firefox makes the majority of that income via their Google partnership
today. Recently, the majority of it was coming from Yahoo.
The browser's market share will ultimately determine the market value of the search partnership, so Vivaldi will likely have a much lower income from it than Firefox, but it's in no way limited by whether they partner with Google or with any other search provider. For a smaller more efficient team, not maintaining their own browser engine, it could easily compare in sustainability to Firefox's income stream.