Not Medical Advice:
It may not kill you, but it is possible; swallowing Visine can be very dangerous, and is not a harmless prank as it is often portrayed on television and in movies!
Taking Visine, in particular its active ingredient, Tetrahydrozoline HCI 0.05%, internally can cause a dangerous lowering of body temperature; nausea and/or vomiting; difficulty in breathing, or even stop it completely; blurred vision; a sharp rise in blood pressure followed by a sharp drop; seizures or tremors; even a coma.
The makers of Visine, Pfizer, warns users to seek medical help, or contact a local Poison Control Center immediately if the product is swallowed.
Visine is designed for use in the eyes, and should only be used in that manner.