Programmed self-assembly of DNA enables the rational design of megadalton-scale macromolecular assemblies with sub-nanometer scale precision. These assemblies can be programmed to serve as structural scaffolds for secondary chromophore molecules with light-harvesting properties. Like in natural systems, the local and global spatial organization of these synthetic scaffolded chromophore systems plays a crucial role in their emergent excitonic and optical properties. Previously, we introduced a computational model to predict the large-scale 3D solution structure and flexibility of nucleic acid nanostructures programmed using the principle of scaffolded DNA origami. Here, we use Förster resonance energy transfer theory to simulate the temporal dynamics of dye excitation and energy transfer accounting both for overall DNA nanostructure architecture as well as atomic-level DNA and dye chemical structure and composition. Results are used to calculate emergent optical properties including effective absorption cross-section, absorption and emission spectra and total power transferred to a biomimetic reaction center in an existing seven-helix double stranded DNA-based antenna. This structure-based computational framework enables the efficient in silico evaluation of nucleic acid nanostructures for diverse light-harvesting and photonic applications.