If you are asking that as the Ivy attaches it tenacles to the trunk, will it take nutrition from the tree, the answer is no. If your asking will the Ivy absorb nutrition from the soil, that would have otherwise been available to the tree, the answer is yes. However, you can easily compensate for the small of nutrition that the Ivy will use. The decorative value of an Ivy cover container and trunk, in my opinion would be well worth any small loss of nutrition. There might be some small concern about the container being shaded by the Ivy's foliage causing the soil to remain wet longer, but if the size of the tree is matched correctly to the size of the container your tree should be OK. BTW, I am a member of the American Ivy Society, and have traveled to many countries of the world with the society, visiting hundreds of private gardens that are not open to the general public. I would say go for it. Why NOT? - Millet