The red wire would be connected to a separate breaker

Yes, called two circuits sharing a neutral, code requires a double breaker be used.

While a shared neutral is allowed, all connections of the white neutral must be spliced, connecting on terminals on devices such as receptacles is not allowed. An open neutral of a multiwire circuit can be damaging to the appliances on the circuit.

Suggested editorial change "Spliced" to "Pigtailed"