This is a good question.
The answer is: sort of.
Right now, you can't set up a custom hotkey in screenshot captor itself to tell it to take a screenshot and then print it.. Though allowing these kinds of custom hotkeys is something I do plan on adding.
However, what you can so is go to the "Post-Capture Options" tab and check the box labeled "Auto print" to have it automatically print every screenshot, and then on the "Interface Options" tab choose "After Capture Show: Stay Minimized". With those settings, when you take a screenshot it will automatically be printed while the program will stay out of your way in the system tray.