in an STM32F407, I enabled USART6's clock in RCC, and set USART_CR1.RE and USART_CR1.TE and USART_CR1.UE.
If I write 0xFFFF into USART_BRR, then write any byte into USART_DR, in USART_SR the TXE bit is cleared and remains so indefinitely; and there's no activity on the respective Tx pin.
If I write 0xFFF7 into USART_BRR, the byte which has been written above is output properly onto Tx pin and TXE bit is set in USART_SR.
All BRR values between 0xFFF8 and 0xFFFF appear to behave in this way.