Dawn is scheduled to fly past Mars on February 18 at 00:29:06 UTC, a little under a week from now. In a few hours it'll be close enough to Mars that the force that Dawn feels from Mars' gravity is stronger than the force it feels from the Sun; that is, it'll fly within Mars' Hill sphere. But Dawn is moving too fast for it to remain in Mars' thrall.
From Mars' point of view, Dawn will approach, speed up, fly within 549 kilometers of it, and zoom back out at exactly the same speed with which it approached. But from the Sun's point of view, Dawn will speed up significantly during the encounter; it'll be boosted into a larger orbit and a more tilted trajectory. That's the magic of gravity assists!
Dawn's approaching Mars from the night side, which would make for pretty spectacular imaging if it were safe to point cameras within a few degrees of the Sun. I expect that if they were really desperate to, the Dawn team could figure out how to take those pictures, but the fact is that Mars isn't a science target for them, and they have more important things to save their cameras for. So we probably won't get any images on approach. If everything goes well, they might take some pictures as they depart, when the Sun is in a safer position, and when the more fully lit images of Mars will provide more value to them for calibrating their cameras, measuring how they perform in space.
One good place to look for updates on where Dawn is predicted to be throughout the flyby is, as usual, Daniel Muller's website; he has a nice page on the mission here. I'll be listening carefully for actual news from Dawn and will post updates here as I get them.