Only when the weight of the ivy is so great that it breaks branches or the stem of the tree.

Ivy can kill trees when it grows thick. The ivy roots attach themselves to the tree and take out the water. The tree dies from lack of water and nourishment.

Sorry but the adventitious 'roots' which an ivy uses to cling to things do not take in any water or nutriments, they are merely devices to cling with. Yes ivy will, when really thick, choke a tree, but it is not the above ground roots which do it. It is the thick evergreen light blocking leaves which do the damage.