Yes, and Yes.
I have my direcTV received connected to the internet, wirelessly. I have had VOD operating for about 2-3 months. It works pretty well. Had some problems with the HDVOD audio synching correctly with the video.
I have the HDDVR receiver. It has a Cat-5 network port in the back. You can hook up your network to this port if you have high-speed internet. It wouldn't be worth it for anything but high speed like a cable modem.
There is no USB wireless connection that will work. The only thing that will work wirelessly is called a wireless gaming adaptor.
Amazon.com: Linksys Dual-Band Wireless-N Gaming Adapter: Electronics
This link is to the version that I have.
This item is available at Best Buy. Most salespeople will not find it in the store. Try the Geek Squad. They will point it out.