Just ask if you need anymore info.
Where to start...
My question is could the arduino wifi sheild transmit real time video
You should build a Robot that can be controlled by Arduino(see below) and add e.g. a wifi webcam like dericam - http://arduino.cc/forum/index.php?topic=90432.0
You can control that remotely as long as you have wifi connection.
I think wifi is not the way to go in a Nuke plant as all the concrete will be reinforced and won't allow signal. Or you should send a dozen repeaterRobots to create a chain of tcp/ip routers. Using a cable is more reliable.
Furthermore be aware that the Arduino and the dericam are not radiaton hardened as far as I know. That means it can be fried just when the video gets interesting and that can be quite fast...