UV damage to internal tissues seems unlikely given that the tartrazine dye they used absorbs strongly in the UV region of the spectrum. You can see this in Figure S1 A & B:
Also the abstract of the article notes that strong UV absorption is likely a prerequisite for this effect:
> We hypothesized that strongly absorbing molecules can achieve optical transparency in live biological tissues. By applying the Lorentz oscillator model for the dielectric properties of tissue components and absorbing molecules, we predicted that dye molecules with sharp absorption resonances in the near-ultraviolet spectrum (300 to 400 nm) and blue region of the visible spectrum (400 to 500 nm) are effective in raising the real part of the refractive index of the aqueous medium at longer wavelengths when dissolved in water, which is in agreement with the Kramers-Kronig relations. As a result, water-soluble dyes can effectively reduce the RI contrast between water and lipids, leading to optical transparency of live biological tissues.
However this kind of research into the effects of absorption bands on the transmission properties at interfaces might ultimately bring about more effective sunscreen formulations.
> UV damage to internal tissues seems unlikely given that the tartrazine dye they used absorbs strongly in the UV region of the spectrum
To expand: "the most hazardous UV radiation has wavelengths between 240 nm and 300 nm" [2]. While tartrazine has a lambda max at 425 nm in water [2], it has a second ridiculously-convenient peak around 260 nm [3].
TL; DR It should be mildly UV protective ceteris paribus.
like an x-ray, I'd risk that for a one-off doctors appointment, but I'd probably not risk it on my body at all times. maybe there are safer dyes that have the same effect