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I suppose so....Doppler shift is due to motion towards or away from the observer. In this case away from. Now, technically speaking, Hubble shift is due to the expansion of spacetime itself, and not the movement of the individual galaxies, which are at rest w.r.t. spacetime in regards to the expansion. However, if you wanted to call the expansion and the subsequent redshifting of the light a "species" of Doppler shift, caused by that movement of spacetime (not the galaxies), then I suppose you could. But really, it seems to be a matter of semantics here. And the whole idea of separating the two, Hubble expansion and Doppler shift due to the actual movement of the galaxies, was done for a specific purpose. To differentiate the two types of redshift and allow the astronomers to calculate both, without getting either mixed up. They have two different mechanisms of causation...one being the stretching of spacetime and the other being the movement of the galaxies (due to gravitational forces etc) within spacetime. That's why it was important to separate the two to begin with.
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