If a pipe extended from just above the ocean floor to outside the atmosphere, would water be sucked up it by the vacuum beyond the atmosphere? If a hole was made in the pipe, above sea level, how would that affect the flow of water? Would it stop it completely?
No, the water would not be sucked up.
Even if you take a pipe with vacuum, closed the top and dipped the open end of that pipe in water then the water would only rise 10 meters. After that the 'pull' from your vacuum is in balance with the force of gravity acting on a 10 meter water column.
Maybe needless to say: The top of the atmosphere is way higher than 10 meters.
Ask yourself this: why doesn't the vacuum of space just suck away our atmosphere? The reason is because of the earth's gravity, which pulls on the gas envelope around the planet to keep it in place. The phenomenon we call 'air pressure' is also the result of this.
The tube will only fill until its contents are being pulled down by gravity with the same force as the rest of the atmosphere. If the straw starts out with air in it, then the air in the straw will be pulled exactly as hard as any other column of air that size, and so the water will not move at all. If there is no air in it, only about 10 meters of it will fill (like Hennes said), only until the amount of extra water in the tube weighs the same amount as an equivalent area of the atmosphere does.
From what I understand, vacuums such as space don't actually "suck" or "pull" at all.
When a box of compressed air is introduced to a vacuum, the air molecules are actually being pushed by the other, higher-pressure air molecules into the low-pressure region of space. This means that, with regards to your question, there is a limit to how high the water can rise. This is determined by the force of air pushing down on the water to force it up the tube, balanced with the force of gravity pulling the water back down.