Google’s Gmail is set to soon (within the next day or so) begin accepting emails from… people without email accounts?

No. How it works is a Google + User can now send an email to you (through Google+), and you do not know who it is from.  And in turn, they do not really know your email address, unless you reply to them.

Mashable.com has a pretty good take on this:

Starting in about 24 hours, any Google+ user will be able to send an email to your Gmail account if you have not given them your email address. The update that Google announced Thursday automatically turns on this option, meaning if you do not change your settings, your email inbox will be open to messages from potential strangers.

Don’t panic, grab your towel and breathe. There is an ‘opt out’ feature that you can implement if you don’t fancy the vast unknowns of cyberspace stalking you.

Full article from Mashable.com with instructions to disable this new (potentially creepy) feature: http://mashable.com/2014/01/09/gmail-changes-fix/