Gemini, links to https://www.sciencedirect.com/science/article/abs/pii/S10759... that says that bacteria split the tartrazine in your guts, so I guess no.

Also as the main article explain, to get the effect the concentration must be quite high, like a 5% solution for 12 hours. That's like 50x the concentration of tartrazine in fake orange juice, that is probably dangerous to drink or take a bath.