Generally speaking, it won't kill you if you drink eye drops by accident, but it may give you a period of hard time. There are some eye drops that only contain sterile saline solution. They are not harmful because they can ingested.
But other eye drops can be dangerous. For example, if you drink Visine eye drops that contain Tetrahydrozoline HCl 0.05%, it will lower your body temperature to dangerous levels Making breathing difficult or even halting it entirely. So, you shall take eye drops seriously.
Some kinds of eye drops are not harmful if you drink them by accident. But some kinds of eye drops which caontain tetrahydrozoline can do harm to you. It is said that visine eye drops contains tetrahydrozoline, so you can't drink visine eye drops. If you drink visine eye drops by chance, you should go to see a doctor immediately otherwise it will cause serious problems to your body.