Ivan,
Very interesting question! Quick follow up question: At what point would you propose the text entered is "sent" to GA?
Either way you're going to have to code up a custom solution with JavaScript, but I'm thinking this is possible. The issue is that there will have to be an action that triggers the event. It does not have to be a click, but instead could be when the text box gets deselected.
Just know that you don't necessarily need a click event to send the event. You can fire the event using JavaScript that watches for SOMETHING.