And if you also want to see Google+ notifications when you are not using any Google product, you can check out Surplus, which is a free Chrome extension for you to get Google+ notifications everywhere, whether you are opening a Chrome browser or not.
After installation, you can see a Surplus button on the right of the address bar in your Chrome browser, the button will be red when there are notifications from your Google+ account. Clicking the button, you will see the notifications in the same format as what you can see from the Google black top bar, besides, there will be also a "Share" button, clicking on which, you can update and share your profile status, with photos, videos, links and locations as what you can do on the Google+ site. What is more, Surplus will automatically add the URL of the current page in the share box, but you can disable this feature on the Settings.
Besides the Chrome browser, you can also enable desktop notifications, with or without sounds, so that you can get Google+ notifications and update your status whether you are using Chrome or not.
Surplus said it supported multiple Google+ accounts, but which was not stable. During my test, it only showed the notifications of the first account I signed in, and I even failed to click any single notification to expand it.
By the way, you need to log in your Google account in your Chrome browser to use the Surplus extension.