Yes. The term 'Dark Side of The Moon' is a misnomer, as the more appropriate name for it would be 'the Far Side of The Moon'... The reasons for this are as follows:
1) The moon orbits the earth at a speed basically identical to it's rotation, just the same way that Mercury orbits the sun at the same rate as it rotates, and thus shows only one face to the sun, and the moon only shows one face to the Earth.
2) The Earth on the other hand rotates FAR faster than it's orbit around the sun (thank goodness, or that side would be really HOT and the other side would be REALLY cold), and through this rotation is constantly changing the face it has turned toward the sun. This rotation is what gives the illusion of the sun 'moving' through the sky, when in relation to the Earth an all the other planets, it is completely unmoving, holding the gravitational center of the entire solar system.
3) Now considering the prior two points, AND the fact that the Moon's orbit does not in ANY way coincide with the position of the sun in relation to the Earth, save in the same way that any predictable, repeating motion can be said to have 'relation' to any other predictable, repeating motion (like being able to predict eclipses), it should become obvious that the far side of the moon would HAVE to regularly experience the light from the sun.
Now having said all that, consider the following: A Lunar eclipse (the Earth passing directly between the Sun and the Moon, causing the moon to be obscured almost entirely by the Earth's shadow) is the exact opposite of a Solar Eclipse, when the Moon passes directly between the Sun and the Earth, causing the Moons' shadow to cross the face of the Earth, darkening the areas fully covered by it nearly to night. (note I didn't say that the Earth was entirely obscured by the moon's shadow, it's just too small to cast such a shadow) Now since you know about Solar eclipses, and that such an occurrence happens when the Earth is one one side of the moon (the side that is always turned toward the Earth) and the Sun is on the other, or 'Far Side' of the Moon, don't you think there would be sunlight on that 'Far Side' while it's blocking that sunlight from the Earth? Well, there you go. (^_^)
Hope that answered your question WITHOUT boring you straight to sleep... Well, unless you really need the rest, in which case - You're welcome, and Sweet Dreams!