Can I play the Supporter "Copycat" when it's the only card in my hand?
Yes, you can. Shuffle your deck, then draw cards equal to the number of cards in your opponent's hand.
Source: HeartGold & SoulSilver FAQ (2010-02-11), PUI Rules Team (2010-02-11)
Can I use the Supporter "Copycat" when my opponent has no cards in his or her hand?
Yes, you can. Shuffle your hand into your deck, but don't draw any cards.
Source: HeartGold & SoulSilver FAQ (2010-02-11), PUI Rules Team (2010-02-11)