Releasing the parking break is fine, however, If the particular airline records the 'Doors closing' time via ACARS too, then you can get the peculiar situation of the aircraft showing to of pushed whilst the doors are still open ! which takes some explaining
Again depends on the programming of the ACARS.
Some ACARS use only brakes off, some use the later of brakes off or doors closed.
For us, 5 minutes after STD requireds a delay code, and our ACARS uses the later of doors closed or brake release.