Is it possible to start and/or join a Google Hangout on Android without also having a Google+ account?
From the support page
Do users need a Google plus account to use Hangouts?
No, but some features—using apps in video calls, sharing photos, and using circles to control who can reach you and how—require a Google+ profile. See the following for more information: Hangout video call features available with or without a Google+ profile and Hangouts Chat vs. Google Talk
For Google app users the additional information states:
Although Google+ provides a superior experience, it is not required for Hangouts for Google Apps to work.
In the Android gapps package it appears to require a Google account, but only Google plus to send pictures.