In Corlies et al. (2020), which analyses instrumentational requirements for a possible future Titan orbiter mission, a modelled transmission function for Titans atmosphere as function of wavelength and chemical species is shown in their Fig. 1 (Can plots from papers on the arXiv legally be used here?).
That figure clarifies that Titan's tholin hazes possess significant absorption opacities in the optical, overlapping with Rayleigh and Mie-scattering, but stronger in effect. This effect is weakening strongly the deeper into the infrared one progresses, with a small high-absorption bump at 3 $\rm\mu m$. The weak have continuum opacity however reaches deep into the near-infrared, trapping very minute amounts of the planets emitted infrared heat. The latter process is however dominated by methane.
Additionally, Doose et al. (2016) had a look at the single scattering albedo $\omega_0$ of Hazes, which gives rise to reflection of incident sunlight. In the entire atmosphere this quantity is very high, $\omega_0>0.9$ at $750$ nm, but with a complex behaviour, dropping to smaller values above 0.9 at $500$ nm.
Together with the previous answer in this thread, I synthesize the following picture for the role of Titan's hazes onto its atmospheric energetics:
1.) Hazes readily absorb UV radiation, making it available for atmospheric photochemistry. Photochemical products rain out downwards into the troposphere, but barely contribute to further energetic activity.
2.) In the optical hazes scatter and absorb both strongly. Both factors lead to a blockage of sunlight towards the surface and hence the conclusion must be that Titan's hazes force an anti-greenhouse effect in the stratosphere.
3.) In the infrared, Hazes are unimportant for the energy balance. Here Methane keeps the planet warm-ish with a mini-greenhouse effect using the remainder of sunlight left by the hazes.