They will. It happened to me. I flew on a "buddy pass" that I bought but which are given to airline employees to fly free on a standby basis. I was on a plane from St. Petersburg to Warsaw, thence to Frankfort and London. In Warasw I got bumped from a plane ready to take off because of my standby status, even though I'd been on the plane since St. Petersburg. Not only that, I had to wait on hard-plastic unupholstered banana seats 26 hours for the next flight to Frankfort. Not having a visa I could not leave the airport, Still, it was a mixed bag because along two legs of my journey, upon request, I got upgraded to business class.
Ah ... but that is distinct from someone being so bumped who is from the general public.
Will they toss such a person off, presumably without their consent and some consideration as compensation?