Depends.

Virginia creeper is native and has co-existed with native trees for eons. 

It does not grow tightly or wind around a tree choking it, like Asian wisteria, Japanese honeysuckle or bittersweet. It also does not smother a tree like English ivy. (All are considered non-native invasive vines.) Virginia creeper just hangs loosely on a tree.

It will co-exist just fine with most trees, however Virginia creeper vines can get quite large and heavy, so there could be an issue. If you have a tree that, say, is at the edge of a woods and is already leaning over, that would be a problem, especially in storms. The extra weight of the vine and, if it is in leaf, the leaf surface catching the wind, could pull it over. (Of course, ice could bring down a leaning tree, too.) 

On the other hand, Virginia creeper is a native vine with berries that feed wildlife. And it has great fall color.

A landscape of at least 50% native plants is a good goal for everyone. 

Ellen