No. The game seems to limit players to the elements provided on the game grid itself. Using the basic three elements would also ensure the greatest number of potential players since the more exotic subsets would required even greater training on the part of the players and reducing the number of people able to effectively participate.
Fire-benders can produce unlimited fire so it does not need to be provided. Chunks of Earth are slotted up and are constantly renewed during a match. Water is made available from a section of the field and able to be tapped by water-benders, so there is no need to use water from below the arena.
Since the goal of the game is to push players backward from the field, it makes sense use only the most basic forms of the elements in a manner that would most effectively drive back the opposing team. Limiting the types of damage being dealt makes it possible for the uniforms being used to be able to effectively protect the players.
Professional bending is a sport designed around speed, coordination, teamwork, precision and accuracy, so using large amounts of any element which might take too long to manipulate would only make you vulnerable to attack and removal from the field. This is also true of most of the subset powers which are also equally challenging for most non-adept benders.