Yes.
In this case, all the STM32 sees is a UART connection - it neither knows nor cares whether that came via USB, or from a Real RS232 port, or from anything else.
So, as far as the STM32 is concerned, the FT231XQ (or whatever) is irrelevant - it's all just UART comms.
The built-in UART Bootloader is described in Application Note AN3155, USART protocol used in the STM32 bootloader:
https://www.st.com/resource/en/application_note/an3155-usart-protocol-used-in-the-stm32-bootloader-stmicroelectronics.pdf
You can also write your own custom bootloader - see, for example Application Note AN4657 STM32 in-application programming (IAP) using the USART:
https://www.st.com/resource/en/application_note/an4657-stm32-inapplication-programming-iap-using-the-usart-stmicroelectronics.pdf
A complex system that works is invariably found to have evolved from a simple system that worked.
A complex system designed from scratch never works and cannot be patched up to make it work.
