Are you envisaging a wired connection to each desk? If not, I suppose you would need a wireless Arduino per desk which would add quite a lot to the complexity and cost. Otherwise you could wire them back to a central Arduino, where you're presumably multiplex them.
I am envisaging as the first rough model an Arduino at one of the students' desk. The one who has the worst attendance. It is to bring awareness to his tardiness and engineer him to coming more punctually.
However, as the future model I envisage that it will be a button connected to a small microcrontroller (Atmega or something of the nature) which has been programmed by an Arduino to transfer the data to the computer.
Anyway, assuming you have some solution for the students' button presses to be communicated in real time back to an Arduino which is connected to a PC, it just needs to write a message to the serial port to tell the PC that the button has been pressed.
Surely this would be possible without an Arduino as well. (An Atmel microcontroller that has been programmed by Arduino)
An application on the PC would receive these messages and take whatever action you defined.
Would I need to make such an application? It seems like that should be able to be done with the currently exisiting Twitter Library and than from there with Zapier to automatically SMS it to students or perhaps with Twilio.
Given all the work you've gone to to acquire this information I'd be inclined to log it to a database so that you can do something useful with it such as produce attendance reports,
and if you want to send a text or post a tweet or whatever then you can launch an application on the PC to do that. Naturally, the application will have access to the PC's clock and all the other services you might need to do that.
Don't get how that would automatically work. I don't want there to be a person who has to do any data entry.
(Personally, if my school had given me a button that sent me a text when I pressed it, I'm sure that as soon as the novelty factor wore off it would be abandoned as pointless, distracting and a waste of money. But that's nothing to do with the technology.)
Well, it's always worth a try.