NO ! - Ivy in itself will not damage the unless the tree is very young, or old and weak. In both cases the ivy naturally effectively overtakes the host tree. The problem for weakened trees is the ivy increases the in balance of the tree structure producing a 'sail effect', making a weak tree prone to more sever storm damage.
Depending on your tree and its age the ivy can easily co-habituate, but should be pruned after it reaches the main outward branches. This may be anywhere from six to twelve feet above grade level. If your sycamore tree is healthy there should be no problem. Seek out professional advice from a regional botanical university. Do not rely on a local contractor, or decorative plant specialist.
Rampant ivy growth may indicate that the tree is unhealthy when a tree is very old, and possibly dying back. Consult an professional agriculturist, or tree surgeon, to set the limits, and ascertain a pruning schedule to balance the ivy spread for a two to three year schedule.