Yeah. It'd be great if this was just an option in the Surface app. Clicking the button like you would a pen to turn the Surface into draw mode seems like a pretty natural way of doing things.
@kidpiglet If you want a really blunt and simple way of achieving the same result hit the Windows key, type "Device Manager" and open it (I recommend pinning it to Start so in the future you won't need a keyboard to do this). Then go down to "Human Interface Devices" and expand it. It'll bring up a list of mice, touch screens, pens, etc. If you're on a Surface Pro 3 it should have "HID compliant touch screen" about halfway down the list. Unless you have multiple touch screens connected that should be your Surface's built in touch screen. Right click it (or hold the pen down on it for a second), then select "Disable". Leave Device Manager open, that way you can just switch to it from the task bar, right click "HID compliant touch screen" again and then hit "Enable" to turn the touch screen back on.
Before you actually do this make sure to have a mouse and keyboard on stand-by (one of the Surface's touch/type covers or a standard keyboard/mouse will do). Rebooting the Surface won't re-enable the device so if you do this and then accidentally lose the pen you're going to need an alternative input method to turn it back on.
It's a bit annoying doing it every time but if you're struggling with Autohotkey I recommend this method because running .bat files you don't understand is potentially hazardous. They can open the door to doing pretty much anything so unless you really trust the source it's not a great idea to have them doing things you don't understand. This method, while annoying compared to just hitting the purple button, has you manually doing it so you can see that the only thing happening is HID compliant touch screen being enabled/disabled.