In the case of ordinary schemes, all coproducts exist, so given any constant diagram $D_S:C\to \operatorname{Sch}$, the colimit over $D_S$ is isomorphic to the coproduct of $S$ over the connected components of $C$. In the homotopical setting, colimits over constant diagrams are much more interesting, representing tensors by homotopy types.

Do all colimits over constant diagrams exist in the ∞-category of derived schemes or spectral schemes? Where can I find a proof?