I can see Firefox following suite. Just embed CPython and route it through that; given that they are struggling to match the Javascript performance of V8 it seems they might welcome a free diversion.
Chrome following suite is more questionable. V8 is the current king of the ring in JS performance, but Google is widely known to be a supporter of Python. I can imagine them amiable to the idea of unifying their server side glue with the client. Besides; they have shown time and time again to make 'strategically strange' moves in order to help advance the general state of the internet. When it comes to google if the internet wins, they win.
Opera would be wise to support it as a differentiating feature. They need all the tricks they can pull to stay relevant.
The bugaboo to me is Apple. They have Nitro, which is right up with V8 in most benchmarks, and support for languages which have benevolent dictators living in their enemy's quarters doesn't sound like an Appleish thing to do. I doubt they would peacefully hand over any control.
Of course if we do stumble into a multi-client-side-language-choice Renaissance it will be Adobe with the most to lose.