A: Hey Jake,
Short answer? No, the new Apple TV doesn't run with Boxee.
Long answer? The new Apple TV doesn't run boxee anymore since there's no hard drive in it. Very much like the iPhone with limited capacity, there are limited options at your disposal when it comes to attempting to "jailbreak" it. For now, we have not seen any news of a Boxee jailbreak or anything like that in the hacking community.
In this case your only other option is the Boxee Box, the Logitech Revue, or the Roku. While we've reviewed all of these items, Boxee still seems like the best combination of features & hardware specs vs. price. Your final option is to grab an older 160GB ATV and run Boxee, but the slow ATV processor has been known to cause issues at times, so we'd be careful with that.
If you own the old Apple TV and would like to install Boxee on it, you can check out the full installation instructions over at Boxee.