Bring Your Own Materials
The interviewer asks: "Tell me about your time at XYZ Company."
Your response: "Sure! I actually put together a few visuals that will help me illustrate a project I was particularly proud of. It'll also help me explain my approach..."
Not only does this help you steer the conversation, but it demonstrates how you communicate, how you break down complex concepts, and ... well ... it's oh-so-wonderfully-polished.
It's better to have the materials ready and available. Diagraming in real-time can be a distraction, and waste valuable time - but if it's your only option, practice your diagrams in advance.
And of course, the all-important disclaimer: don't share confidential info that isn't yours.