The main reason for the eyepiece shutter isn't that light coming in through the eyepiece would reach the sensor (or film). The main reason is that light entering the pentaprism backways could affect the light meter, which has its sensing device located above the eyepiece, at the rear of the pentaprism.
Put the camera on a tripod or similar and aim the camera at something pretty dark, like outdoors in the evening. Look through the viewfinder and check which exposure the metering system considers correct.
Now take you head away, let a lamp glow outside the eyepiece and check which exposure the camera calculates while the lamp is lit. You can see it on the top LCD, when the lamp is preventing you from looking through the viewfinder. Usually, the exposure calculated is a bit different, since the camera thinks the subject is brighter than it is, with stray light coming in from the wrong direction.
An easy way to prevent this is to set the exposure in M mode, while you look through the viewfinder, and then take the shot. Then it doesn't matter if the meter is confused. But this does of course take that light doesn't change too much, so it's not well suited for time-lapse across the day.