Can you catch sleeping Aniimo?

You skip the fight entirely, and a sleeping target is far easier to catch than an awake one.

Sleep stacks with the other stealth bonuses. Staying undetected on the way in already raises your odds, and coming at the sleeper from behind adds the back attack bonus on top, which applies whether the Aniimo is awake or asleep. So walk round to its back before you throw rather than lobbing an Aniipod from wherever you happen to be standing.

The one way to throw this away is to wake it. An Aniimo that spots you and engages loses the sleeping bonus, and being alerted lowers its capture rate below what an ordinary undetected approach would give you. At that point you are back to weakening it in battle like any other wild catch.

Is a sleeping catch guaranteed?

Not reliably. In some cases the displayed chance on a sleeping Aniimo climbs to 100%, even with the cheapest capture pod. In others it is only much higher than normal and stops short of a certain catch.

You do not have to guess. The game shows the exact catch chance when you aim, so read the number before you throw. If it says 100%, a basic Aniipod is enough. If it says anything less, the pod can still shake and fail, so line up the back approach or bring a higher tier Aniipod for anything you would hate to lose.

Not settled: Whether a sleeping Aniimo is a guaranteed catch is not settled: the displayed chance sometimes reaches 100% with the cheapest pod and sometimes stays below it, and what decides the difference is not known.