UART- Tx/Rx Line cut detection
If "functioning properly" means proving that Tx and Rx lines are not open circuit then "no". To check this requires "something" at the far end however, even with something at the far end you cannot simply know that a line open fault is due to Tx, Rx or both.

You could develop a form of TDR (time domain reflectometry) but this seems overkill.

If you are looking for shorts between wires or to ground then it can be done at one end of the link.