If an Animagus eats something that is harmful to the Animagus' form would it harm them?

This is almost certainly never addressed in canon.

Personally I would lean towards no but the only answer would be maybe

Is a human magically transformed into a dog really a dog for the sake of chocolate being poisonous to them, what happens to stomach contents when someone transforms. Without knowing precisely how the magic works I do not think anyone could say for certain.

i dont think they would die because to maintain the animagous form takes effort. So if sirius were to eat a bunch of chocolate he might become sick but then would revert to his human form before dying and then be perfectly fine.

A witch or wizard in Animagus form will eat the food of their animal form:

An Animagus is a witch or wizard who can transform at will into an animal. While in their animal form, they retain most of their ability to think as a human, their own sense of identity and their memories. They will also retain normal human life expectancy, even if they take their animal form for long periods of time. However, feelings and emotions are simplified and they will have many animal desires, feeding off whatever their animal body craves, rather than demanding human food.

The above quote comes from the e-book: Short Stories from Hogwarts of Heroism, Hardship, and Dangerous Hobbies, Chapter One: Animagi.

One would then assume that if they ate something toxic to their animal form it would indeed be harmful to them.

However, since most Animagi are not in their animal forms for that long, I would expect they would merely transform back into their human form prior to eating.