I don't know how they are designed. A google may help you out or maybe someone here. But the breaker monitors phase to phase and each phase to neutral. I don't believe a strait 240v gfci without the neutral is made. They all have the neutral.
Correct, a gfci breaker will not function without a neutral connection, even with a straight 240 v load that does not require a neutral, the gfci breaker does.