Can Alpha Aniimo bosses be captured?

The order is what matters. Against ordinary wild Aniimo you soften the target and throw while it is still standing. An Alpha boss refuses that entirely. The fight has to finish first, and only then does the capture window open. So the usual routine of chipping a creature down and watching its Break gauge is not what gets you an Alpha. Winning the fight is.

Then comes the part that catches people out. Beating the boss earns you the attempt, not the creature. A low catch rate means a plain throw at a downed Alpha will often fail, and a failed throw on a boss is an expensive way to learn. Count your pods before you pull an Alpha, not after it is lying there.

Making the low catch rate stop mattering

Aniipods come in tiers, and higher tiers carry higher base capture rates. The upper tiers are the ones capable of catching boss Aniimo at all. The Aniipod Ultra ends the argument: a flat 100% capture rate, Alpha Aniimo included. If you have one, the boss's low rate is irrelevant.

Stocking them is the real work. Standard Aniipods are the base tier and can be farmed infinitely, and basic ones can be crafted through Homeland systems using mined shells. Your Homeland also produces Aniipods over time through facilities staffed by assigned Aniimo, and those keep working while you are offline. To move up the ladder, a merchant converts lower-tier pods into higher-tier ones at two for one, and Glimmer buys higher-tier pods directly. Farming the base tier is therefore never wasted. It is the raw material for the pod you actually want to throw at an Alpha.

Giant units are a separate case

Do not assume every oversized Aniimo works this way. Giant unit Aniimo cannot be captured at all. There is no post-fight window for them and no pod tier that changes it. Alpha bosses are the ones worth saving your best pods for.