Serial LCD and Serial GPS

Im wondering if it is possible to have both a serial LCD and serial GPS connected to the arduino serial port at the same time. (id like to advoid software serial if I can.)

Im assuming it would work, since the LCD will only need to receive data I can connect the LCD to the TX pin of arduino.

And the arduino will be receiving data from the GPS, I connect the GPS to the RX pin of arduino.

Would this work, how would this affect programming the arduino over the serial port? I would have to disconnect the GPS and LCD before programming?