Yes, the wireless UART modules are designed to be connected to the UART of a microcontroller or similar device. It is not recommended to connect a UART to one of the transparent modules.
Transparent modules do not have any built-in protocol or memory, so all protocol aspects are managed by an external microcontroller. It is very simple to output data on a microcontroller’s UART and so many engineers try this. The issue is that the UART protocol was designed for a wired environment, which does not have much random noise. The RF environment is extremely noisy and UARTs cannot manage that noise well. It is recommended to develop a noise-tolerant protocol and to “bit-bang” an output on the microcontroller to send the data to the transparent modules. See AN-00160: Considerations for Sending Data over a Wireless Link for more information.