If you drilled a hole to the liquid core of the Earth, would all the molten metal shoot out onto the surface?

It's hard to say for certain.

My guess would be no, because I don't see what source of pressure would cause the molten iron to rise. Billions of years of pressure doesn't get undone in a couple minutes.

But then again, it's all really guess work at this point. The farthest we've drilled into the earth is about 19 kilometers if I remember correctly. We haven't even hit the mantle yet.

I am pretty sure it would if the hole was big enough. The problem would be to cooling effect the surround earth would have on the molten lava from the core. All you have to do is look at the various kinds of volcanic eruptions that there are to see the effect of a hole to the core.

It's possible but I doubt it would just shoot out. If anything like this occurred, it'd probably be a slow process...

Of course, it'd be hard to predict due to other things like volcanoes though.

If you were to make a perfectly pressured tube, it'd just leak lava.
Unless you kept said tube pressurized and went deep enough, then as you get toward the more pressurized areas its going to come out faster when you open the tube.