Q: In Homeworlds, if I sacrifice a piece, is that piece available immediately in the Bank to use as a result of that action?

… For example, if I sacrifice a small yellow, can I immediately use that small yellow to become a star system being traveled to with that move?

A: Yes, when you sacrifice a ship, it goes immediately into the Bank, and is available to use as a result of the action. In fact, it’s key to several different important game strategies.

In addition to your example above, where the sacrificed yellow is used immediately as a destination star…

One can also sacrifice a green, return it to the Bank, and (if it’s the smallest available) immediately grow that piece back again.

Less common, but still an option: one could sacrifice a blue, and then use it to turn a ship into the blue piece that’s just been sacrificed.

Red is the only power for which this is not relevant, since sacrifice of a red ship does not use up any pieces from the Bank.