Are there any microcontrollers in the STM32F4xx series that support the NSS pulse mode in their SPI controllers?

No. ST tends to stick to the same IP version of the modules within a family, even if upon introducing newer models of that family there are already newer versions of the same IP in other families.

The NSS pulse is in 'F0, 'F3, 'F7, 'L0 and 'L4 SPI (and probably 'H7 but that one has quite a lot of changes in the SPI).

JW