Yep, a US Neo Geo will play Japanese games, and in English at that! (Unless you get one of the few strictly Japanese-only games like the quiz games.)
Unfortunately, some games will be censored too, like having white blood in Metal Slug.
You can also get your system modded by Jeff Kurtz so you can get S-video output, dip switch settings, and a country switch, so you can switch your Neo from US mode to Japan mode. Also, Jeff's mod might be able to let you play games uncensored and in English, but I'm not sure about that one. If his mod will let you play games in MVS mode, I imagine you can.
I know with MVS games, you can play games uncensored and in English, however. (I own an MVS, not an AES, so I'm not talking about the mod from my own experience.) Jeff is JMKurtz on this board, and I'm sure several people here can recommend his work.