OK, so right now, you have a 60A/240V plain breaker in your service panel.
It feeds a "hot tub subpanel" with a 60A/240V GFCI breaker in the sub.
This hot tub subpanel does not have any room for 20A breakers.
You want to install a 20A multi-wire branch circuit (MWBC) to power two 120V subcircuits.
You know that requires 20A overcurrent protection (breaker).
You want to accomplish that by changing the main-panel breaker ($10) instead of the GFCI breaker ($80).
Yes, this is absolutely fine. The 20A supply breaker will provide the overcurrent protection and the 60A GFCI will provide the GFCI protection.
This is similar to having a 50A feed to a 200A-breakered subpanel, when Code requires a disconnect switch. The main breaker is a) a disconnect switch and b) a 200A overcurrent device. We only care about a).
It feeds a "hot tub subpanel" with a 60A/240V GFCI breaker in the sub.
This hot tub subpanel does not have any room for 20A breakers.
You want to install a 20A multi-wire branch circuit (MWBC) to power two 120V subcircuits.
You know that requires 20A overcurrent protection (breaker).
You want to accomplish that by changing the main-panel breaker ($10) instead of the GFCI breaker ($80).
Yes, this is absolutely fine. The 20A supply breaker will provide the overcurrent protection and the 60A GFCI will provide the GFCI protection.
This is similar to having a 50A feed to a 200A-breakered subpanel, when Code requires a disconnect switch. The main breaker is a) a disconnect switch and b) a 200A overcurrent device. We only care about a).