YES!!!!! The purpose of a drip edge is so that the water does seep under the shingles and rot out your sheathing that is under the shingles. You might think that with the pitch of the roof, there is no way that water will get up under the shingles, but water is weird in that it likes to "cling" to things as long as possible before it falls. The drip edge prevents that water from clinging to the bottom side of the shingle/sheathing. As a rule of thumb, I like to put drip edge all the way around the roof, but at the bare minimum, you need to put it on the lower edges of the roof.
