how many processor cycles/time does it minimaly take to transmit 1 Byte via Serial?
No, it is not true.

You are assuming (wrongly) that the CPU is doing the UART communication.  It isn't.

The UART is a completely separate piece of hardware inside the chip.  It runs by itself.  The CPU merely places the byte to transfer into a special function register (SFR).  The UART then takes that and clocks it out through the IO pins at the right rate for the serial communication.  While that is going on the CPU is free to perform other operations.

The CPU can then either consult another SFR to determine if the transmission has finished, or utilize an interrupt that the UART will trigger when the transfer has been completed.