Chlorpromazine is a "typical" antipsychotic, i.e. one with significant activity as a dopamine antagonist (in addition to the serotonergic and antihistaminergic effects you find in 2nd-generation-antipsychotics).
The problem with typical antipsychotics is that once you exceed a certain threshold (when a significant portion of dopamine receptors have been blocked) you start developing unpleasant side-effects, most notably parkinsonism (i.e. temporary shaking similar to a patient with Parkinson's disease. "Real" PD results from the death of dopaminergic neurons; therefore, reversibly blocking dopamine receptors with antipsychotics temporarily produces similar effects). If high doses are taken for extended amounts of time, some side-effects may become persistent.
Thus, they have mostly been supplanted by 2nd-generation antipsychotics.
Re: GABAergic activity, chlorpromazine was invented almost 70 years ago, and has seen widespread use in clinical practice since atleast 60 years. Its pharmacology has been studied extensively, and if it had any significant affinity for binding sites on the GABA receptor, it probably would have been noticed by now. Remember, there was *a lot* of commercial interest in exploring the structure-activity-relationship of the phenothiazine class of drugs in order to find more well-tolerated antihistamines, antiemetics, antipsychotics and sedatives.