Do you expect the aromatic hydrocarbons to react in a similar way to the cyclic alkenes, since the are both cyclic compounds and have double bond?

No.

Explanation:

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In this case, the answer is no due the fact that cyclic alkenes contain π bonds that are not conjugated or partially conjugated but not abided by the Huckel 4n+2 π electron system in a conjugated structure.  However, aromatic hydrocarbons are likely to react with electrophilic species to promote electrophilic substitution yet cyclic alkenes does not.  

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