If an animal eats it, wouldn't it be combusting the captured carbon to produce CO2/H20/energy? I don't think you'd want to feed it to anything, but just let it be buried or be pushed under the earth's crust.
Yes, they don't even need to eat it, just from decomposing versus growing corn you can measure the rising and falling cycles of co2 at different times of the year for north america. I think Azolla is still less effort to grow than most plants, which might still help out if it ends up being used for animal feed.