Is damping material necessary for a speaker having such a small cabinet volume?

Wait.. Is this something you bought designed to be wall mounted? if so, follow manufacturer's recommendations. 

In a speaker enclosure, damping material lessens reflections, but also increases internal volume, so it depends.  I have seen some delightful, tiny speakers use internal wadding, to good effect. 

Best,

E

I am confused.

Are you talking about in-wall speakers? or wall mounted speakers?