Quick answer: NO, at least not directly and it will depend on what kind of system you're trying to study. The reason is that QE is really a material rather than a molecular property. A quick glance on the wikipedia page on QE will tell you that. You can certainly compute oscillator strengths for phonon absorption. However, quantum efficiency, say in the case of a solar cell or light-harvesting device, involves more than just the probability for a chromophore to absorb a photon and undergo some photo induced process.
Moreover, QY depends on relative rates of deactivation vs emission and deactivation depends on a bunch of mechanisms, on the aggregation state, specific solvent interactions... waaaaay easier going to the lab and measuring it.
I gather you're looking at poly-thiophenes, such as P3HT, for solar cell materials. P3HT's band gap is ~2.3eV. and the photoemission around 600-700nm depends upon aggregation: http://pubs.rsc.org/en/content/articlepdf/2008/EE/B805643A
The approach to calculate radiative, internal and intersystem crossing (and QY) by semiempirical methods (INDO) was realized in our department by prof. Artukhov, Mayer, Plotnikov, Danilova. There are many restrictions in this approach (parametrization is only for C, H, O, N, S, F, Cl, Br, B). It is not Gaussian. But, if the system - is simple organic molecule (without metals, and negligible two electron contribution), then you get quite accurate results. If it's interesting, I will help you to contact with prof. Artukhov. The program is free, but without graphical interface.
You can view publications of prof V. Ya. Artyukhov. For examle:
Spin‐Orbital Interaction in Molecular Complexes of Naphthalene with Anthracene Derivatives DOI: 10.1023/A:1019264118932
Three-center integrals of one-electron operator of a spin-orbit interaction DOI: 10.1007/BF02508964
and many others, where the possibilities of approach are described.
Tomorrow I'll ask prof. Artyukhov user manual and executable files of his program (English version). I have only Russian version of the program. Maybe he will register on the ReserchGate and answer you himself.