Can a part of a compound be a reducing agent?
For accounting purposes, we can assign oxidation numbers to all the atoms. Oxygen could be -II in all species here, then sulfur would be +IV in $\ce{SO4}$ and -II in $\ce{Cu2S}$ (oxygen and sulfur are in the same group and both are more electronegative than copper, so assigning the same oxidation number in $\ce{Cu2S}$ and $\ce{Cu2O}$ makes sense). Oxidation numbers of atoms in elements are zero, and the copper in both compounds would be +I to balance out the -II of the chalcogens.

Once you are in agreement with your discussion partner on these oxidation states, you can make a statement about which atoms undergo oxidation or reduction: Sulfur gets oxidized, and copper in both copper compounds gets reduced. 

In cases where only one atom in a compound changes oxidation states, or when all changes are in the same direction, we do talk about the compound being reduced or oxidized. For example, it is common to say that when you oxidize an aldehyde, you get a carboxylic acid (and when you reduce it, you get an alcohol or an alkane). 

On the other hand, if you hydrate an alkene, some folks don't consider that a redox reaction.