UART in AVR Microcontrollers
Simply, you can. 

In addition to charansai's answer, if the MCU supports hardware UART then it becomes easier. Since the transmit/receive process is done via the hardware itself, you don't have to wait for a transmit or a receive process to complete. Depending on the setup, the module raises either an interrupt or a flag once the process is complete.

Even if a software-UART is used, it's still possible by using some programming skills.