Recent years witnessed significant performance advancements in deep-learning-driven natural language models, with a strong focus on the development and release of Large Language Models (LLMs). These improvements resulted in better quality AI-generated output but rely on resource-expensive training and upgrading of models. Although different studies have proposed a range of techniques to enhance LLMs without retraining, none have considered computational argumentation as an option. This is a missed opportunity since computational argumentation is an intuitive mechanism that formally captures agents' interactions and the information conflict that may arise during such interplays, and so it seems well-suited for boosting the reasoning and conversational abilities of LLMs in a seamless manner. In this paper, we present a pipeline (MQArgEng) and preliminary study to evaluate the effect of introducing computational argumentation semantics on the performance of LLMs. Our experiment's goal was to provide a proof-of-concept and a feasibility analysis in order to foster (or deter) future research towards a fully-fledged argumentation engine plugin for LLMs. Exploratory results using the MT-Bench indicate that MQArgEng provides a moderate performance gain in most of the examined topical categories and, as such, show promise and warrant further research.