If the 50 or 75-moves-rules do not apply and there's a mating position, then the arbiter can't declare the game drawn. Here's what FIDE Laws of Chess say (emphasis mine):
5.2.2 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.
9.3 The game is drawn, upon a correct claim by the player having the move, if:
9.3.1 he writes his move, which cannot be changed, on his scoresheet and declares to the arbiter his intention to make this move which will result in the last 50 moves by each player having been made without the movement of any pawn and without any capture, or
9.3.2 the last 50 moves by each player have been completed without the movement of any pawn and without any capture.
If quickplay finishes apply, which should be announced in advance by the tournament organiser/director, then (emphasis mine):
Guidelines III. Games without increment including Quickplay Finishes
III.5 If Article III.4 does not apply and the player having the move has less than two minutes left on his clock, he may claim a draw before his flag falls. He shall summon the arbiter and may stop the chessclock (see Article 6.12.2). He may claim on the basis that his opponent cannot win by normal means, and/or that his opponent has been making no effort to win by normal means:
III.5.1 If the arbiter agrees that the opponent cannot win by normal means, or that the opponent has been making no effort to win the game by normal means, he shall declare the game drawn. Otherwise he shall postpone his decision or reject the claim.
However, if the game is Blitz, then the above don't apply (emphasis mine):
III.2.2 These Guidelines shall apply only to standard chess and rapid chess games without increment and not to blitz games.
To sum up, the answer to your question is no because you are talking about Blitz games. Generally, in rapid and standard games, if the side with the most time just shuffles pieces around and quickplay finishes apply, then the game can be drawn.