Is a certain amount of stress healthy?

Likely yes, but some. Some stress is necessary to stimulate a person to perform. This can occur in exercise, and hectic situations. In fact, many medical tests, like glucose challenge, and Dexamethasone suppression test for cushing's are stress tests of a sort. They are designed to see if the body has a healthy response. But too much stress os any kind can cause more harm than good so do things in moderation.