The type VI secretion system (T6SS) of Gram-negative bacteria has been involved in various processes, notably bacterial competition and eukaryotic cell subversion. Most Pseudomonas aeruginosa strains possess three T6SS gene clusters, but only the function of the first T6SS (H1-T6SS) has been clearly elucidated. It is involved in the secretion of three toxins (Tse1 to -3) that target bacterial competitors. In the case of the H2- and H3-T6SS, no clear function has been assigned, and only one effector has been associated with these systems. Yet the H2-T6SS was proposed to promote P. aeruginosa internalization in nonphagocytic epithelial cells. Although the H2-T6SS genetic organization is conserved across P. aeruginosa isolates, one feature is the presence of an additional transcriptional unit in the PA14 strain H2-T6SS cluster, which is divergent from the core H2-T6SS genes. A specific set of four genes encodes an Hcp protein (Hcp2), a VgrG protein (VgrG14), an Rhs element (PA14_43100 or RhsP2), and a protein with no homologies with previously characterized proteins (PA14_43090). In this study, we engineered a P. aeruginosa PA14 strain carrying an arabinose-inducible H2-T6SS on the chromosome. We showed that arabinose induction readily promotes assembly of the H2-T6SS, as seen by monitoring Hcp2 secretion. We further studied the secretion fate of VgrG14 and RhsP2, but these were not detectable in the extracellular medium. We finally investigated whether activation of the PA14 H2-T6SS gene cluster could influence phenotypic traits such as internalization in eukaryotic cells, and we reported noteworthy differences compared to strain PAO1, which may be accounted for by the described genetic differences.