I actually think that’s potentially one of the most compelling aspects of Google+. Right now, Google bakes G+ into most Google properties via the black nav bar. This undoubtedly spurs a lot of usage. What if the next phase is to take it a step higher? Go right to the browser itself? They just started promoting their G+ Chrome extensions… We’re one step away.
Of course, Google would never admit to wanting to bake G+ into Chrome right now. But they’d be foolish not to be at least thinking about it. They already have users logging into Chrome now for syncing, etc. We’re already much closer to this happening than most probably realize.
I imagine it will happen if G+ doesn’t maintain the growth and adoption that Google is hoping for. We’ll see an option to log into G+ from within Chrome itself. Maybe they’ll even release a special version of Chrome to avoid those who will inevitably throw a shitfit if they try to fully bake it in. Or maybe they’ll just point out that Chrome isn’t actually open source, Chromium is. And you’re free to use that. There’s a reason both exist.
Above all else, Google must be paranoid that Facebook is working on their own browser with deep social integration. I would be.
As for deep Android integration, I’m sure we’ll see that before the deep Chrome integration. It’s happening already with ICS.
From a business and integration perspective, these would both be smart moves. But they’ll also remind people even more of 90s-era Microsoft. Google has to tread carefully here.