Closure of surface-subgroup-free right-angled Artin graphs under complete graph amalgamation

Let $A(\Gamma)$ denote the right-angled Artin group associated to a graph $\Gamma$, and let $\mathcal{N}$ be the class of graphs such that $A(\Gamma)$ does not contain a closed hyperbolic surface group. A complete graph amalgamation of two graphs is their union when their intersection is a complete graph; the two graphs are induced subgraphs of the union. Closure conjecture. The class $\mathcal{N}$ is closed under complete graph amalgamation. This would provide a key step toward a graph-theoretic characterization of right-angled Artin groups that do not contain closed hyperbolic surface groups; the conjecture's resolution is not specified in the source.