Her ability works a lot like Bravery's old Passive Effect, drawing a card each time you play a card. But unlike Bravery, Catty does this no matter how many cards you're holding. However, she only does it whenever you summon a monster, so Spells don't trigger the effect, but cards summoned through cards like Igloo or Lamp will.
Because of this, Catty can pair very well with Onion San, as placing Onion San while Catty is on your board will make you draw 3 cards because of Onion San's tentacles, but only if there is enough room for the tentacles.
However, they don't pair that well if you already have a lot of cards in your hands. It only really works if you have 2 at most, excluding Catty and Onion San.