Can I save an A/B test?

Yes, you can save your A/B test as a draft in Email marketing > A/B tests.
When you click on Create A/B test you will be taken to an A/B test creation page. After setting up the message, you can save it as a draft for later.

Legacy editor

No, an A/B test is a part of the newsletter creation process and is not an individual type of message. Therefore if you leave the A/B test settings page while creating the message, it will be saved as a draft. The A/B test versions are always a part of a created message.