Here is a (mostly) non-Android solution for you.
You'll need to (sign up for and) use If This Then That.
Create a recipe.1
Your This will be the Gmail channel, specifically the Any new email trigger.2
Your That will be however you'd like to be notified. I like Pushover but SMS will work just as well. You'll use the Send me an SMS action (or send a notification for Pushover).3
Now you can be notified of new messages in your Gmail without even actually having Gmail on your phone.4
1 If you prefer, you can just use this recipe (SMS) or this recipe (Pushover).
2 If you don't want to be notified on every new message, there are other triggers you can use, like "New email from" or "New email from search" that can be more specific.
3 Unfortunately there is no Google+ channel. There a lots of other channels for lots of other services.
4 IFTTT triggers usually don't go off more than every fifteen minutes, so don't expect your notification to be instantaneous.