Yes you can. But it will be pixelated in full screen mode. The experience won't be as good either.
The iPad requires more power to charge it than the iPhone or iPod, and most computers (especially older ones) don't provide enough power to their USB ports in order to charge the iPad at a sufficient rate - it will probably still be charging, just slowly (it will be a bit quicker if the iPad's screen is off).
The wall charger that came with the iPad is the most efficient way to charge it - and though it's more powerful than the one that comes with the iPhone, you can also safely charge iPhones (or iPods) with it (http://support.apple.com/kb/HT4327)