Yes, VPN works really well for MLB, NHL and NBA.
NBA being the most restrictive of the three I have tested with via VPN.
MLB I just needed to point my VPN router to a different state, and then I can watch my local MLB team. NHL doesnt seem to matter. Router was local and I'm still able to watch my local NHL team with no restrictions.
NBA was a different story and took a few additonal steps.
During the free NBA trial week, most of the US based games were still blacked out. National broadcast I beleive.
I signed up for a International League pass and then had no further restrictions.
The steps I had to perform to get the NBA to work on the Apple TV was the following with some decent pricing:
1) Pointed my VPN dd-wrt router to India.
2) Pointed my MAC to my VPN dd-wrt router.
3) Sign up for International NBA league pass via my MAC. (India NBA price was a bit cheaper than other countries. $139 USD during the trial week)
4) Once I signed up for my NBA International pass, I pointed my VPN router to the UK.
5) I then switched my Apple TV DNS to point to my VPN router.
6) Switched the itunes store on the apple tv to point to the UK store.
Note: If you dont switch your itunes store, you will not be able to login using your NBA international account. If your not in the US, you can probably skip this step.
7) Signed into the NBA app on the Apple TV using my International League pass id.
8) Enjoying games since.
Hope this helps.