A saturated organic compound has general formula CnH2n+2. Halides count for H, and if the formula contains nitrogen, we subtract NH before the determination. Every 2H's less than the saturated formula corresponds to a degree of unstaturation. And each degree of unsaturation corresponds to either a double bond (i.e. C=O, C=C, C=N) OR a ring junction.
For benzene, the molecular formula is C6H6. A saturated alkane with 6 carbons would have a formula of C6H14. Thus benzene has 4 degrees of unsaturation. The representation of benzene as 1,3,5-cyclohexatriene makes these degrees of unsaturation very easy to see.
So aromatic compounds are by definition unsaturated.
