Yup, I should think that would make your allergy clear.
As a side note, Coriander is often known as (From Thai “phakchi”) as well so you might want to try saying that if the point doesn't seem to be getting across.
EDIT: @Chocolate points out that when it's a spice its and when it's a raw leaf it's . Assuming you are allergic to both you might want to mention both.