No, if some idiot at a tournament was playing on in a pawnless Q vs Q game, you could have the TD declare it a draw due to insufficient losing chances.
Likely no opponent would be this rude though.
A TD could declare the game drawn but he woud be in violation of the laws of chess and quite wrong.
Ref: https://www.fide.com/fide/handbook.html?id=171&view=article
Article 5.2.b The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.
It is of course possible to checkmate an opponent's king with a K&Q. I'm sure worse blunders have been made, even in recent memory. Players are free to play terrible chess within the constraints of the tournament. It is not the arbiter's job to pass judgement. Their job is to enforce the rules.

@little charles: Because people have life outside of the internet.