This idea is really good. Hear is a chance to reduce transactions fee of Bitcoin. It's helps lot for so many members. Who have not aware in exchanges their coins, this type of service really helpful to them. Hear we can do peer to peer transactions very easily when we need.
The transaction may happen but the bitcoin is not moving at all on the blockchain, so what you're trading is mostly private key or a raw transaction as mentioned above. It is a bad idea as the sender can easily create a copy of the private key and then move the money first when he get internet access. You need something like opendime if you want to be safe, but obviously you can't do it through sms.