I think most of the creatures should be atleast somewhat aggressive, though if a large force is going by and there are few of them, they might decide to hide. I also think semi-tame animals would be good, so on human worlds bears are used to humans and will not easily attack humans (except maybe a lone marine or marine squad) while the covenant would not be recognized and immiedietely attacked.The inverse would be true on some covenant worlds.
Animals should also be somewhat smart; if you tell a unit to move where a bear is, the bear might move out of the way, if you repeatedly move a unit, or multiple units to where the bear is though, it will become aggressive. This concept should also apply if the animal or it's home (if it has one) becomes surrounded. Another trigger for aggression could be the sounds of combat or accidental fire hitting the animal while units are firing at a different target.
I'll also mention that not all battlefields will be in "civilized" places where animals are aware who elites or humans are, so they may not fear them. Additionaly, the logic of animals is not always the same as the logic of humans.
A Halo Wars Story: Once upon a time, there was a light bridge. On that light bridge, there were many covenant. When the UNSC turned the bridge off, the covenant fell. The End.