So you have some computer running a terminal emulator, but that computer only has a USB serial port. You want to plug your converter cable into that USB port and connect the RX, TX and GND pins at the D-shell connector to the corresponding GPIO pin on your PI. ... and the answer is ...maybe.
https://elinux.org/RPi_Serial_Connection
Check the voltages at the D-shell. These old converter cables typically output a 5 volt TTL signal at the D-shell. The signals at the D-shell connector are derived from the USB 5 volt power. These serial converters generally do not boost the voltage, but 5 volts is still enough to damage a PI's GPIO. You will need some kind of simple level shifter to interface the converter's 5V logic to the Pi's 3.3 V logic.
https://elinux.org/RPi_GPIO_Interface_Circuits#Level_Shifters
If you build a level shifter, your idea can safely work. Of course, there is also the lazy man's method.
https://www.adafruit.com/product/954
lsusb
and show the display. You might need the drives