I would avoid ivy in general.
Hedera helix is known to produce irritating sap, as well as possibly causing neurological and/or gastrointestinal issues if consumed. Even if it's not eaten directly by the reptile, I've heard stories of feeders eating ivy and then poisoning the animal when eaten. These are largely anecdotal accounts, but it's not something I'm comfortable risking... and I'm the crazy person that uses all sorts of untested plants!