I know that if q1 and q2 indicate rotations, then q2q1 represents the composite rotation of q1 followed by q2.
but what about addition?
I believe quaternion addition is similar to vector space translation (in 4D), but have no geometric meaning.
depends on what you use the quaternions for. quaternions with only imaginary part can be used to represent vectors, and then, quaternion addition results in vector concatenation, a.k.a. translation.