This is examined experimentally in the paper
Ultrafast Photoisomerization of Photoactive Yellow Protein Chromophore Analogues in Solution: Influence of the Protonation State
Agathe Espagne, Daniel Paik, Pascale Changenet-Barret, Monique Martin, Ahmed H. Zewail
The photoisomerization corresponds to the twisting of the double bond shown below.
The figure above shows the de-protonated (anionic) form. The protonated (neutral) form has a proton attached to the oxygen anion on the right end of the molecule.
They find that the excited state lifetime of the protonated (de-protonated) chromophore varies significantly with the solvent viscosity (polarity) but not the polarity (viscosity).
It is not surprising to me that the shape of the excited state potential energy surface varies significantly with the protonation state. Seth Olsen has shown this clearly for the chromophore of the green fluorescent protein in high level quantum chemistry calculations. These surfaces can be described by a simple two-state effective Hamiltonian (see here). The key physics is that de-protonation tunes the system away from "resonance" between the two underlying valence bond states. Generally, when one is close to resonance the ground and excited state have small net dipole moments and one expects a weak coupling to the polarity of the solvent.
A key challenge is constructing the simplest possible effective Hamiltonian which can describe the excited state dynamics including the effective of the solvent viscosity and polarity.