Yes, because addiction changes the brain in fundamental ways, disturbing a person's normal hierarchy of needs and desires and substituting new priorities connected with procuring and using the drug. The resulting compulsive behaviors that override the ability to control impulses despite the consequences are similar to hallmarks of other mental illnesses.
In fact, the DSM, which is the definitive resource of diagnostic criteria for all mental disorders, includes criteria for drug use disorders, distinguishing between two types: drug abuse and drug dependence. Drug dependence is synonymous with addiction. By comparison, the criteria for drug abuse hinge on the harmful consequences of repeated use but do not include the compulsive use, tolerance (i.e., needing higher doses to achieve the same effect), or withdrawal (i.e., symptoms that occur when use is stopped) that can be signs of addiction.