Using SoftwareSerial for the serial monitor
Short answer: no.

Pins 0 and 1 an an Uno are directly wired to the PC communication chip. You could make a board that was wired differently and connected SoftwareSerial to the PC, but you would have to switch it back to pins 0 and 1 when uploading to the arduino somehow. 

On an arduino leonardo "Serial" for communicating with PC over USB is different from "Serial1", which is connected to pins 0 and 1 on the board. You can use both simultaneously, so if you really need to use hardware serial and PC comms at the same time, I recommend you buy a leonardo.