Hi,
I will re-state for the sake of clarity.
The Messages App on the Mac can have an iMessages account Active and this can send iMessages just from the Apple ID if you don't have an iPhone.
An iPhone has an app also called Messages and if you activate it it will register the iPhone Number with the iMessages Server.
The App can also enable SMS/MMS messaging and it will decide how to send a "text" based on where the recipient is registered with. (i.e. iPhones that are registered and Apple ID will get iMessages but non Apple phones will get SMS).
Later versions of the iOS version of Messages can Forward as it is called the SMS/MMS messages to the Mac over the same LAN.
This enables the Mac to Send and Receive SMS.
Posts here are not really clear about whether Messages on the iPhone can send mixed SMS/iMessages out to a mixed group of iPhone and non iPhones (presuming Numbers only).
It is not something I have tried myself.
This article suggests how it can be done http://www.pcadvisor.co.uk/how-to/mobile-phone/how-send-group-texts-from-android -iphone-3472964/
So to be clear:-
The App is Messages and the Account/Service/actual text is called iMessage.
Text (SMS) chatting is not something I did before iMessages came along for text chats on an iPhone.
I was much more into using a Mac and iChat.
In Messages, for an AIM chat, you should be able to add a number of people/Numbers to the "To" spot to create a group.
I happen to have used a spoof number as the second and the AIM Auto error message account as the other.
You get this double circle in the Side bar to indicate there are more than one contact involved.
There are specific SMS apps out there for computers and some are Mac ones.
However that seems a bit like buying the iPhone just to make something that seems possible work by using something else.
9:06 pm Tuesday; January 26, 2016
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad