Can this transmit through walls?

yes. I have my router in my living room and the Roku is in my bedroom. no problems with quality.

will this pull in over the air tv ?

Sure! That's what mine do. If you're in a fringe reception location like I am, you may need a good roof antenna, or signal amplifier, or both. note: I use MSWin7 Media Center software. After you've done the Control Panel work to get the system to recognize your device/s, just tell Media Center it's an antenna, and not a cable feed.