AT module and RN2483: not working with my Linux box

Do you think that when power goes up, that GPIO will remain in high impedance? No glitch?

Unfortunately you cannot be sure there won't be any glitch at power-up because of the high impedance. As @DrAzzy said, only a pullup will give you the guarantee that the TX line of your STM32 is at a known state at power-up.
Another way to avoid any confusion may be to hard reset the RN2483 after having configured the USART interface (pin 32 of RN2483), but then you need an extra wire...