It does not seems to be supported by Construct, if it was, it would probably be in the Browser plugin and I can find anything. However, it is possible with javascript, using the window.print() function. So you can try using the "Execute javascript" action, also from the Browser plugin.
But I don't think you'll be able to print the canvas in it's current state anyway. You'll probably get what the page looks like before the game loads, not much. It requires more work, taking a snapshot, inject that image somewhere on the page, print that, then remove it and return to the game, not worth the trouble.