Originally Posted by iwoloschin
They are correct. It is impossible for your phone to receive texts, or any other network-based communications, while "offline." That's a physical impossibility, as to communicate on a network, you need to actually be connected to the network.
Now, maybe you're talking about WiFi only, with Mobile turned off? You won't get text messages on your phone's number, but you can use Google Voice to send/receive texts via WiFi only. It'll require using a different phone number, but it's pretty easy to set up.
OP, do not listen to this absolute load of misinformation that is quoted!
I use the Hangouts app for texting only, and I am not signed in to any three of my gmail accounts at all, and I am able to send and receive texts. Even when I have wifi and mobile data turned off i can still send and receive text like normal.