Could an armless person play at OTB Tournaments?

Of course.

   Any TD would ask how he GOT to the tournament. A friend, aquintance, family member?

A person with limited arm control entered a speed chess competition.  His games were played seperated from the masses, and he would call out his moves and I would move the piece.  

I played a blind player.  The same procedure was used.

As long as there is no cheating and it does not interfer with the other players, any method used to accomodate persons with disabilities is acceptable.

Long time ago I saw a player in a tournament who had a brain problem and could not make the moves by himself.  He had a person to help him, he said the moves and the helper did the moves to him.  

In Poland there is a player with severe muscle dystrophia, Lukasz Nowak (https://ratings.fide.com/card.phtml?event=1166760). I have played him several times in the OTB tournaments when he was in 1700-2000 range (now he's 2300+). The procedure is that his father makes moves for him, funny thing being that at the beginning the man knew next to nothing about chess. Specific arrangments differ. During one local tournament Lukasz was allowed to play at home, and his opponents came to him. During Warsaw championships he played on stage, which gave more room to place him, reclining on his side in a special wheelchair, in a position from which he saw the board best.