Yes, all you need is a GSM radio with a serial port (the modems are now well below £100) but you would need a prepay account function, to fund the outgoing messages.
Both the above sites seem to be prepay sites. The 2nd one should make good money, at 30 euro cents per message...
I think that a number of people looked into this, a few years ago before every half decent phone could browse the internet, and gave up on it for various reasons. I even "worked out" a way to transmit weather radar images using several text messages... Almost nobody in GA will pay for anything which they can get free elsewhere.