No it wouldn't.

why? that's the main reason people give when saying console gamers shouldn't play with PC gamers

It still doesn't mean it's unfair. You failed to give a reason as to why it would be unfair.

aimng with the mouse is more accurate that aiming with a control stick, thus giving PC gamers an advantage over console gamers (mouse for PC, controller for console). This therefore indicates that the PC gamers familiar with using the computer to play first-person shooters will have the advantage over console gamers with the same amount of familiarity with the console controller. This makes it unfair.