Cat grass actually helps them vomit up hairballs and other stuff they don't want int he tummies. My Wellington is asthmatic and he eats grass all the time - I have never noticed it triggering an attack.
It would depend on what your cat is allergic to and where you keep the grass.
If the grass is kept outside, even for a short period of time to help it grow, it will contain pollen, dust, fungi and mold.
Inside only, it will still contain dust, fungi and mold - possibly different varieties though.