Is it possible to Log new Incidents via SMS Messages as you can with Email? Send a text to listener?
Due to the technology that has SMS messages only going to and from actual phone numbers/cell phones, and the small limited format of the messages it is not natively possible to create Incidents from these messages. So no, you cannot do this within the Cloud Service Management System.
As an alternative you could set up an SMS gateway on your network, which requires either a Cell Phone or Cell Phone modem with a dedicated number, Then it could be possible to convert the SMS messages to actual emails and send them into the system via the email listener.
Searches on the Internet can provide many possible SMS to email solutions.