I'm an opera singer and a colleague told me she puts an ice pack on her neck to reduce vocal fold edema after a performance. Is there any credence?

Highly unlikely. The vocal folds are behind the skin, the platysma muscle, and the thyroid cartilage. It is highly unlikely that an ice pack would reduce the swelling of these folds after singing. With proper singing technique, proper breathing, singing within your normal range and proper voice rest and not warming up too much before a performance, you should be fine. The ice pack would not harm you, however.