It might not make you drowsy, but it has much more serious effects, and if you consume it, you should call the Poison Control Center.
“The active ingredient in Visine eye drops is Tetrahydrozoline HCl 0.05%. Swallowing this substance can result in a number of nasty effects, including:
Lowering body temperature to dangerous levels
Making breathing difficult, or even halting it entirely
Blurring vision
Causing nausea and vomiting
Elevating and then dropping blood pressure
Causing seizures or tremors
Sending the ingester into a coma “